Tuning.....kind of an interesting theory
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Re: Tuning.....kind of an interesting theory
One question not really answered above is why a perfect 5th might need to be raised 2 cents. It's because the pitch of an equally tempered keyboard 7 half steps up is 2 cents flat from a "pure" 5th.
Taking A = 440 Hz, then a "perfect" E, in pythagorean tuning, would be 3/2 times that, or 660 Hz, which is 2 cents sharper than an equally tempered E 2^7/12 times 440, which is @ 659 Hz.
As far as our ears are concerned, I confess to being around so many keyboards and guitars and electric basses, which are all ostensibly tuned or fretted to "equal temperament," (the fact that it doesn't turn out that way in practice please let us leave to another discussion just for the sake of this observation), that "pure" major thirds, in a pythagorean 5/4 sort of way, actually sound flat to me until I can get away from keyboards and guitars long enough for my ear to re-acclimatize.
Taking A = 440 Hz, then a "perfect" E, in pythagorean tuning, would be 3/2 times that, or 660 Hz, which is 2 cents sharper than an equally tempered E 2^7/12 times 440, which is @ 659 Hz.
As far as our ears are concerned, I confess to being around so many keyboards and guitars and electric basses, which are all ostensibly tuned or fretted to "equal temperament," (the fact that it doesn't turn out that way in practice please let us leave to another discussion just for the sake of this observation), that "pure" major thirds, in a pythagorean 5/4 sort of way, actually sound flat to me until I can get away from keyboards and guitars long enough for my ear to re-acclimatize.
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Re: Tuning.....kind of an interesting theory
Yeah, I failed to distinguish between Hz and cents. Your 4 cents/1 Hz ratio looks about right, at least around the A=440 pitch. Funny that since 100 cents = 1/2 step, the actually "size" of the cents gets larger and larger as you go higher, but smaller and smaller as you get into the lower ranges.BopEuph wrote:I think you misunderstood. He was saying that his Korg was off by 1Hz, and he had to set it to A=439 to get the right tuning. That's a faulty tuner.
The difference from 439 to 440Hz is just under 4 cents (I believe). While almost indiscernible by the untrained human ear, a tuner WILL pick it up.
Middle C (when A=440) is 261.63Hz. The C above is 523.25Hz. The 1200 cents between the two span 261.62Hz, so they are each about .22Hz. The C below middle C is 130.81, so the 1200 cents between those two span only 130.82Hz and are each about .11Hz. Sounds pretty complicated to build an electronic device to measure, huh?
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Re: Tuning.....kind of an interesting theory
Well said, Robert.
I have the "perfect pitch" gene or whatever. You are absolutely correct that it has zero value for tuning intervals. It's a nice parlor trick, and great for those years of ear training. Comes in handy when transcribing, as well.
But it doesn't help me play in tune any better.
I have the "perfect pitch" gene or whatever. You are absolutely correct that it has zero value for tuning intervals. It's a nice parlor trick, and great for those years of ear training. Comes in handy when transcribing, as well.
But it doesn't help me play in tune any better.
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Re: Tuning.....kind of an interesting theory
Actually, some people are very sensitive to the difference, and some situations make it stand out. I bought the Korg just before playing for a musical where bass guitar and bassoon often had doubled lines. When I was with my tuner and the bassoonist was with hers, I was always just a little above her, and it was fairly easy to tell. After stopping to listen to her against the group for a few minutes, I realized that she was usually dead-on pitch almost all the time. I also felt that I was staying sharp, so I pulled my pitch down a bit, and we meshed. We got together with a couple of others who had these tuners and checked it out. The others registered the same, and mine was off by 1 Hz.Todd S. Malicoate wrote:GC wrote:I once had a Korg CA-30 that had to be set to 439 to get the same reading that other CA-30's got at 440. I didn't think it was possible, but it performed consistently 1 Hz off in side-by-side tests.Sounds like a wash to me. Remember, a difference which makes no difference IS no difference.BopEuph, in the previous post, wrote:unless you have trained your ear with lots of ear training, the untrained human ear can't hear a difference of about 4 cents. So, the two cents thing will only be heard by people with the best pitch.
When I have the tuner play sound and adjust the pitch, I can tell a change of 1 Hz fairly easily. With the preponderance of musicians using tuners as reference points, I wonder how many folks out there are using defective tuners and don't know it, thinking that the tuner can't be wrong. Tuners are easier to use than tuning forks and probably don't vary as much, but they're obviously not perfect either.
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Re: Tuning.....kind of an interesting theory
Thanks, Doc...Doc wrote:Steve Curtis is right - just play in tune.
Amen.Doc wrote:(Check out some top notch barbershop recordings, and you'll see what tuning really is.)
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Re: Tuning.....kind of an interesting theory
We're talking apples and oranges. I was suggesting to James that a tuner would confirm if he was really flat (I think he estimated A=435) and that his band director was "lowering his pitch." On the off-chance that he had a Korg that was a bit "out," he would still at least have a reasonable point of reference (at least a better one than his back-talking roommate with perfect pitch). You're talking about a mis-adjusted tuner causing a problem when you rely on it to play in tune with other players who are using a well-adjusted tuner. Obviously a problem, especially on a fretted bass with no real chance to listen and adjust "on the fly." A perfect tuning pitch is a must for fretted bass playing, but I would think you would get it from the piano in that situation.GC wrote:Actually, some people are very sensitive to the difference, and some situations make it stand out. I bought the Korg just before playing for a musical where bass guitar and bassoon often had doubled lines. When I was with my tuner and the bassoonist was with hers, I was always just a little above her, and it was fairly easy to tell. After stopping to listen to her against the group for a few minutes, I realized that she was usually dead-on pitch almost all the time. I also felt that I was staying sharp, so I pulled my pitch down a bit, and we meshed. We got together with a couple of others who had these tuners and checked it out. The others registered the same, and mine was off by 1 Hz.
Perhaps some folks are using defective tuners, but if they rely on them and not their ears I think they're missing the point of these devices. As Robert pointed out, there's no substitute for ears...tuners ought to just make it easier for everyone to start "on the same page."GC also wrote:When I have the tuner play sound and adjust the pitch, I can tell a change of 1 Hz fairly easily. With the preponderance of musicians using tuners as reference points, I wonder how many folks out there are using defective tuners and don't know it, thinking that the tuner can't be wrong. Tuners are easier to use than tuning forks and probably don't vary as much, but they're obviously not perfect either.
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Re: Tuning.....kind of an interesting theory
Tuning is...old men in stripped vests wooing my grandmother?sc_curtis wrote:Thanks, Doc...Doc wrote:Steve Curtis is right - just play in tune.
Amen.Doc wrote:(Check out some top notch barbershop recordings, and you'll see what tuning really is.)
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Re: Tuning.....kind of an interesting theory
"Just" intonation says raise the fifth two cents. That's smaller than even the most trained musical ear can recognize. That being said, Doc is absolutely right...the overtones really start to ring with the fifth raised a bit. Anyone who's been in the middle of a DCI horn circle working on tuning a major chord can attest to that. Nothing like hearing those notes ringing above where anyone is playing...close your eyes and you'll swear there's an organ sounding high notes.Doc wrote:Regarding raised fifths, you do not have to have special ears or be a piano tuner to hear them. If your band director focuses on lowered thirds, but does not slightly raise the fifths, then he does the band a disservice. PLUS, the tuning "magic" he seeks will NEVER happen. If you want to have a chord in tune (resonate overtones/undertones), the overtone series must be in tune - lowered third, slightly raised fifth. To not raise the fifth means the band is still NOT in tune. SOB, it ain't rocket science. When you begin to hear overtones and undertones being created from correct tuning, the "magic" is happening. Expanded sound. There is stuff there that no one is playing, but it will resonate or be created as a result. That **** is like crack. You want it all the time. There ain't another feeling like. (Check out some top notch barbershop recordings, and you'll see what tuning really is.)
But Doc, it's a question of degree. Of course, on a held major or minor chord the adjustments should be made naturally and people should be able to identify their chord voice. It's a little more difficult, say, in the middle of the first movement of the First Holst Suite when the notes are moving faster. Sometimes you have to say to the 3rd trumpets "Hey, can you lower that B natural a bit in bar 35? You're the third of the F major chord on that release on beat 2, and it would be nice to get some more resonance in that chord."Doc wrote:Actually, every note of the scale has tendencies, and if the band is comprised of music majors, the band director should NEVER have to take valuable time from rehearsal to go over these points. Maybe an occasional reminder, but not to any great length. Of course, if you have people in the band who don't understand the most basic music theory, it will be uphill all the way.
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Re: Tuning.....kind of an interesting theory
I never said that we were talking about the same thing. My issue is peripheral to yours. It was prompted by the "tuners don't lie" (or something like that) comment. They most certainly do, partly because they're fallible, and partly because they're misused. The ear has to be the final arbiter.GC wrote:Actually, some people are very sensitive to the difference, and some situations make it stand out. I bought the Korg just before playing for a musical where bass guitar and bassoon often had doubled lines. When I was with my tuner and the bassoonist was with hers, I was always just a little above her, and it was fairly easy to tell. After stopping to listen to her against the group for a few minutes, I realized that she was usually dead-on pitch almost all the time. I also felt that I was staying sharp, so I pulled my pitch down a bit, and we meshed. We got together with a couple of others who had these tuners and checked it out. The others registered the same, and mine was off by 1 Hz.
We're talking apples and oranges.
Absolutely. I discovered the problem with the tuner because I used my ears and didn't blindly rely on it. I'm just worried that defective ones can cause even more problems. Tuners DO lie if they're defective, and people are lying to themselves if they think that a tuner can tell them if they're on pitch no matter what the chord or progression. I'm in one group where the conductor insists that everyone have a tuner on his stand (which doesn't do a tuba player with an upright bell much good, anyway). He really only uses them as a reference when someone's obviously way off pitch, but I wish he'd just put them away and train everyone better on tuning by ear. He has worked quite a bit on adjustment of the third and fifth, and it has definitely helped.Perhaps some folks are using defective tuners, but if they rely on them and not their ears I think they're missing the point of these devices. As Robert pointed out, there's no substitute for ears...tuners ought to just make it easier for everyone to start "on the same page."
Todd S. "who thinks some of the worst players, tuning-wise, he's played with are the ones staring at a tuner on the stand while they play" Malicoate
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Re: Tuning.....kind of an interesting theory
You are correct...defective tuners do lie. I was wrong to be so sweeping in my comment.GC wrote:I never said that we were talking about the same thing. My issue is peripheral to yours. It was prompted by the "tuners don't lie" (or something like that) comment. They most certainly do, partly because they're fallible, and partly because they're misused. The ear has to be the final arbiter.
Todd S. "thinking a 1Hz misalignment in his Korg would have mattered not at all to James' predicament" Malicoate
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Re: Tuning.....kind of an interesting theory
This thread is a pretty good text book for Musicianship 101.
I'm an old duffer in a community band who finally began to play more or less in tune about 5 years ago.
There is one comment that hasn't been stressed here: One of the main functions of the bass line is to set the tonality. So we really need to lead rather than match what others do. May be a different issue if you're working with soloist, piano, organ, etc.
That came home to me one rehearsal when conductor was having trouble getting clarinets to play their stuff in tune and she said, "Listen to the tuba.... you have to build on that!" Love to hear things like that.
In this same band some of us have tuning problems because conductor wants to tune A=442. They bought a set of bells at that pitch. I can barely get my Miraphone 182 up there... tuning slide has to be all the way in. Then out in the gazeebo when the sun goes down and the horn cools off and goes flat I have trouble. We all have trouble. Second half of concert is always a bit off.
But, I've also found that I can sometimes get the band to tune below A=442 if I fill the reahearsal hall with tones at A=440 before lead clarinet sounds his tuning tone. I'm just trying to get everybody listening to my version of the tuning note. That's fun, and works until bells have a solo passage against some chords.
John Roberts
I'm an old duffer in a community band who finally began to play more or less in tune about 5 years ago.
There is one comment that hasn't been stressed here: One of the main functions of the bass line is to set the tonality. So we really need to lead rather than match what others do. May be a different issue if you're working with soloist, piano, organ, etc.
That came home to me one rehearsal when conductor was having trouble getting clarinets to play their stuff in tune and she said, "Listen to the tuba.... you have to build on that!" Love to hear things like that.
In this same band some of us have tuning problems because conductor wants to tune A=442. They bought a set of bells at that pitch. I can barely get my Miraphone 182 up there... tuning slide has to be all the way in. Then out in the gazeebo when the sun goes down and the horn cools off and goes flat I have trouble. We all have trouble. Second half of concert is always a bit off.
But, I've also found that I can sometimes get the band to tune below A=442 if I fill the reahearsal hall with tones at A=440 before lead clarinet sounds his tuning tone. I'm just trying to get everybody listening to my version of the tuning note. That's fun, and works until bells have a solo passage against some chords.
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Re: Tuning.....kind of an interesting theory
Todd S. Malicoate wrote:
These don't lie...find out where your pitch is "pushed all the way in."

These lie less...
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Re: Tuning.....kind of an interesting theory
Some general comments, since the topic has broadened to tuning in general:
1. All musicians need to train their pitch memory. Having a tuner on the stand during long tones is a useful technique for training our brains to recognize pitch, and for calibrating our ears. Tuners are not evil, and they can support our ability to hear pitch.
2. Tuning chords is not the same thing as pitch memory. Tuning chords is about resonance, not about frequency. The pitches of the interior notes must resonate with the root to create an in-tune chord. (The same applies to overtones within the instrument, which are about resonance rather than frequency.)
3. Pianos have a characteristic sound that is based on the even temperament. The chords are not in tune, but then the way the piano has a more broadbanded sound. Ditto large ensembles in some situations. For example, there is no way a string section will ever be in tune with itself such that it creates the resonance of which Doc speaks. Why? They are all using vibrato. But that is the characteristic sound of a string section, and a section in that case will never sound like an individual. Nor should it.
4. Those who claim "perfect pitch" just have really well-trained pitch memory (or a natural talent for good pitch memory). Those who complain that they cannot abide a group being slightly flat or sharp have over-trained pitch memory and probably need to work on developing a more flexible pitch concept. After all, A being 440 Hz is a convention, not a constant of the universe.
5. Many people who play instruments are amateurs and have neither the talent nor the time to learn pitch memory at that level or to achieve the literacy of which Mitch speaks. But we can all strive for it. I, for one, can't do it. I still need to play through something before I can learn the pitches well, but then nobody pays me to sight-read. (If you need someone to adjust traffic signal timings from intuition rather than analysis, then I'm your man.) Not having this skill does not preclude making effective music. Audiences usually do not have this training, and often cannot recognize good tuning that brings tears of joy to those who can (I can recognize it when others are playing).
6. I can bend the pitches of my Holton at least 20 cents one way or the other. I can bend them 10 cents one way or the other without appreciably affecting the tone. Part of the reason for that pitch flexibility is that the instrument provides a range of resonant frequencies instead of just one. In electronics, we would say that the resonant circuit has lower Q, or that it is a bit broadbanded. If I don't hear the pitches properly, they will be wrong, and I cannot rely on the sound quality of the note to signal when it is right. I once played under a band-clinician type of conductor who insisted he could tell I was off-pitch because my sound was not resonant. What he didn't realize was that on that note on that tuba, the resonant pitch was out of tune. When I played it with the resonance he demanded, the band could not tune to it. But he was happy. Sheesh. There is a difference between frequency and resonance (in this case, the resonance that creates the instrument's overtones). That tuba needed a whole different tuning strategy that I had not yet learned.
7. The resonance of just tuning in chords was discovered in the early Renaissance, if not earlier. Some modern music, however, seeks dissonance and just tuning may not be appropriate in those cases. It's pretty hard to tune a semitone or a major 7th for zero beats, but we can still train our ears for what it should sound like.
8. If one is pushed all the way in and playing flat, it makes me wonder what sort of sound they are producing. Surely they are fighting the natural resonance of the instrument, unless that particular note resonates flat on that particular instrument.
9. The practice room is where we learn the relationship between resonance and pitch for our instruments.
10. Chamber groups are were we learn the relationship between resonance and pitch when playing with other instruments.
11. Large ensembles are where we apply the results of 9 and 10, not where we learn them.
Rick "better at saying it than doing it" Denney
1. All musicians need to train their pitch memory. Having a tuner on the stand during long tones is a useful technique for training our brains to recognize pitch, and for calibrating our ears. Tuners are not evil, and they can support our ability to hear pitch.
2. Tuning chords is not the same thing as pitch memory. Tuning chords is about resonance, not about frequency. The pitches of the interior notes must resonate with the root to create an in-tune chord. (The same applies to overtones within the instrument, which are about resonance rather than frequency.)
3. Pianos have a characteristic sound that is based on the even temperament. The chords are not in tune, but then the way the piano has a more broadbanded sound. Ditto large ensembles in some situations. For example, there is no way a string section will ever be in tune with itself such that it creates the resonance of which Doc speaks. Why? They are all using vibrato. But that is the characteristic sound of a string section, and a section in that case will never sound like an individual. Nor should it.
4. Those who claim "perfect pitch" just have really well-trained pitch memory (or a natural talent for good pitch memory). Those who complain that they cannot abide a group being slightly flat or sharp have over-trained pitch memory and probably need to work on developing a more flexible pitch concept. After all, A being 440 Hz is a convention, not a constant of the universe.
5. Many people who play instruments are amateurs and have neither the talent nor the time to learn pitch memory at that level or to achieve the literacy of which Mitch speaks. But we can all strive for it. I, for one, can't do it. I still need to play through something before I can learn the pitches well, but then nobody pays me to sight-read. (If you need someone to adjust traffic signal timings from intuition rather than analysis, then I'm your man.) Not having this skill does not preclude making effective music. Audiences usually do not have this training, and often cannot recognize good tuning that brings tears of joy to those who can (I can recognize it when others are playing).
6. I can bend the pitches of my Holton at least 20 cents one way or the other. I can bend them 10 cents one way or the other without appreciably affecting the tone. Part of the reason for that pitch flexibility is that the instrument provides a range of resonant frequencies instead of just one. In electronics, we would say that the resonant circuit has lower Q, or that it is a bit broadbanded. If I don't hear the pitches properly, they will be wrong, and I cannot rely on the sound quality of the note to signal when it is right. I once played under a band-clinician type of conductor who insisted he could tell I was off-pitch because my sound was not resonant. What he didn't realize was that on that note on that tuba, the resonant pitch was out of tune. When I played it with the resonance he demanded, the band could not tune to it. But he was happy. Sheesh. There is a difference between frequency and resonance (in this case, the resonance that creates the instrument's overtones). That tuba needed a whole different tuning strategy that I had not yet learned.
7. The resonance of just tuning in chords was discovered in the early Renaissance, if not earlier. Some modern music, however, seeks dissonance and just tuning may not be appropriate in those cases. It's pretty hard to tune a semitone or a major 7th for zero beats, but we can still train our ears for what it should sound like.
8. If one is pushed all the way in and playing flat, it makes me wonder what sort of sound they are producing. Surely they are fighting the natural resonance of the instrument, unless that particular note resonates flat on that particular instrument.
9. The practice room is where we learn the relationship between resonance and pitch for our instruments.
10. Chamber groups are were we learn the relationship between resonance and pitch when playing with other instruments.
11. Large ensembles are where we apply the results of 9 and 10, not where we learn them.
Rick "better at saying it than doing it" Denney
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Re: Tuning.....kind of an interesting theory
Interesting thread.
Tuning is about practice, familiarity, and repetition. Bad intonation, repeated enough times, becomes more acceptable to those exposed to it.
However, I have to disagree with many posters on this thread about the use of tuners on stands. I believe there is a place and an application for them that makes them beneficial. First, I've noticed that some conductors are often "fooled" by the color of a sound when it comes to intonation - often times, a player with a bright sound will be noted as sharp, and player with a very dark sound will be noted as flat - or by the register of the note being played. In these instances I find a tuner to be a sanity check for me when the direction I am receiving is contrary to the actual physics of the sound being produced.
Second, one of the ensembles I've recently joined has a very bad case of playing sharper as a whole as they get louder, but some people are *actually starting to listen* to me for their pitch reference. Again, having a tuner available allows me to perform sanity checks when I KNOW something is off - I don't just check my pitch, but the pitch of the others around me, for my own information. Sometimes you find a group where someone is REALLY off on their relative pitch (like 94% of all Bari Sax players) and having a tuner handy can help identify where the hell he's going to be at certain times.
I'm a pitch Nazi. I don't see the point of playing with good time and a good sound if the pitch is going to be bad. It's kept me from joining groups. It's led me to leave groups. It's the one thing the majority of groups can fix to make themselves sound better by leaps and bounds almost overnight. I view pitch and time as my responsibility in every ensemble I play with, because my failure in one of those areas makes the group sound worse. And with all that in mind, if I can place a $20 piece of technology on my stand to serve as an occasional reference for something that is completely relative, I'm going to do it. I don't live by it, it's turned off more than it's on, but it does have a place and application IMHO.
Tuning is about practice, familiarity, and repetition. Bad intonation, repeated enough times, becomes more acceptable to those exposed to it.
However, I have to disagree with many posters on this thread about the use of tuners on stands. I believe there is a place and an application for them that makes them beneficial. First, I've noticed that some conductors are often "fooled" by the color of a sound when it comes to intonation - often times, a player with a bright sound will be noted as sharp, and player with a very dark sound will be noted as flat - or by the register of the note being played. In these instances I find a tuner to be a sanity check for me when the direction I am receiving is contrary to the actual physics of the sound being produced.
Second, one of the ensembles I've recently joined has a very bad case of playing sharper as a whole as they get louder, but some people are *actually starting to listen* to me for their pitch reference. Again, having a tuner available allows me to perform sanity checks when I KNOW something is off - I don't just check my pitch, but the pitch of the others around me, for my own information. Sometimes you find a group where someone is REALLY off on their relative pitch (like 94% of all Bari Sax players) and having a tuner handy can help identify where the hell he's going to be at certain times.
I'm a pitch Nazi. I don't see the point of playing with good time and a good sound if the pitch is going to be bad. It's kept me from joining groups. It's led me to leave groups. It's the one thing the majority of groups can fix to make themselves sound better by leaps and bounds almost overnight. I view pitch and time as my responsibility in every ensemble I play with, because my failure in one of those areas makes the group sound worse. And with all that in mind, if I can place a $20 piece of technology on my stand to serve as an occasional reference for something that is completely relative, I'm going to do it. I don't live by it, it's turned off more than it's on, but it does have a place and application IMHO.
Rob. Just Rob.
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Re: Tuning.....kind of an interesting theory
I'm wondering who you disagree with...sounds just like what everyone else has been saying about tuners used in ensembles.kingrob76 wrote:However, I have to disagree with many posters on this thread about the use of tuners on stands. I believe there is a place and an application for them that makes them beneficial...having a tuner available allows me to perform sanity checks when I KNOW something is off...if I can place a $20 piece of technology on my stand to serve as an occasional reference for something that is completely relative, I'm going to do it. I don't live by it, it's turned off more than it's on, but it does have a place and application IMHO.
Let me be more clear...I find the players who constantly stare at the tuners, while the ensemble is playing, to be the "problem." They are the most unwilling to change their pitch to help the ensemble, and usually the ones with the worst pitch to begin with (at least in my experiences). They also tend to sit in the first couple of rows...who would have thought?
I don't remember seeing any post in this thread contrary to what you posted. The key words are "occasional reference" and "turned off more than it's on."
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Re: Tuning.....kind of an interesting theory
Yeah, on second read, when I'm not so bleary-eye tired, I guess I don't disagree. Sleep deprivation - it's more fun than one should legally be allowed to have.
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Re: Tuning.....kind of an interesting theory
I agree with all except #4. Your version does not correspond to the literature I have studied.Rick Denney wrote:Some general comments, since the topic has broadened to tuning in general: 1,2,3,4,...
Rick "better at saying it than doing it" Denney
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Re: Tuning.....kind of an interesting theory
an interesting topic. and there are several parts to it. The comments on the band director are quite interesting. Way back when I was in Marching band in college, which was NOT part of the music department, but part of the 'student activities and services' (or some such) department our director spent very little time on the tuning of chords/parts/sections. We spent more time on the ensemble intonation and 'color' that a peice was looking for (the brightness of a march, the heavy distortion of guitar driven rock and roll, the light driving rythmic intensity of latin disco).
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sungfw
- 3 valves

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Re: Tuning.....kind of an interesting theory
What part doesn't correspond?sloan wrote:I agree with all except #4. Your version does not correspond to the literature I have studied.Rick Denney wrote:Some general comments, since the topic has broadened to tuning in general: 1,2,3,4,...
Rick "better at saying it than doing it" Denney
- sloan
- On Ice

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Re: Tuning.....kind of an interesting theory
"4. Those who claim 'perfect pitch' just have really well-trained pitch memory (or a natural talent for good pitch memory)."sungfw wrote:What part doesn't correspond?sloan wrote:I agree with all except #4. Your version does not correspond to the literature I have studied.Rick Denney wrote:Some general comments, since the topic has broadened to tuning in general: 1,2,3,4,...
Rick "better at saying it than doing it" Denney
Kenneth Sloan
