Ab in 1st position

[tbdana]

Sacrilege, I know, but I play high Ab in 1st position all the time. I can do it because my default 1st position isn't all the way in, but a little out. And it's in tune. In practicality, though, I do it only as a passing tone or in a fast passage.

Speaking of fast passages, I also play high Bb in 3rd position very often. Makes ripping a Db major scale a breeze (positions in parentheses): Db (2), Eb (3), F (4), Gb (3), Ab (3), Bb (3), C (3), Db (2). You can play that lightning fast with little effort, all because of the F in 4th and the Bb in 3rd. You don't have to move your arm at all; the whole scale can be played simply by moving the wrist and fingers.

Follow me for more tips 90% of trombonists will disagree with.

[Doug Elliott]

The only time I play Ab in 1st is if I have to turn a page, if that helps to stay in 1st

[harrisonreed]

It's really nice in the David concerto

[Dennis]

It's really nice in the David concerto

As long as the adjudicator isn't looking at you when you play that lick.

I got hammered on that once, and since then I take the Bb and Ab in 3rd.

BTW, please say hello to K-State for me the next time you're in Manhattan.

[Retrobone]

Well. If you own a Kruspe Weschke trombone you can play Ab in 1st and it might even be slightly sharp.

[hyperbolica]

Judging how far in you have to play the G on my horns, I'll never play Ab in 1st. Much more likely to play a bunch of notes in 3rd. Bb is out there very often.

[OneTon]

I almost always play high Bb in 3rd. To my ear, it sounds “right” in 3rd especially for Shiny Stockings and April in Paris. Ab is usually in 3rd (or 7th). I utilize the center slide positions a lot. After all, I am past my prime, sometimes rabble, and frequently wax delusional. But i am grateful to still be playing and learning. Thanks for the tips.

[harrisonreed]

It's really nice in the David concerto

As long as the adjudicator isn't looking at you when you play that lick.

I got hammered on that once, and since then I take the Bb and Ab in 3rd.

BTW, please say hello to K-State for me the next time you're in Manhattan.

Adjudicator?

I will say hi to K-State for you, but only from within the confines of Tall Grass!

[elmsandr]

I’m a big fan of Ab in first for Mozart Requiem…. For many horns I prefer how the intonation sounds over equal temperament.

Cheers,
Andy

[VJOFan]

I’m a big fan of Ab in first for Mozart Requiem…. For many horns I prefer how the intonation sounds over equal temperament.

Cheers,
Andy

+1

And the success rate for the note is much higher with no slide movement…

[baileyman]

If you want to get around well with F Ab G or Bb Ab G, first position is wonderful.

[Dennis]

Adjudicator?

I will say hi to K-State for you, but only from within the confines of Tall Grass!

Yeah, I played it in Solo/Ensemble my senior year of HS. I got downgraded for playing that Ab in 1st..

Well, Konza is part of the University (it's managed by K-State for The Nature Conservancy), so that will work. I hope you're enjoying Ft. Riley.

[harrisonreed]

Adjudicator?

I will say hi to K-State for you, but only from within the confines of Tall Grass!

Yeah, I played it in Solo/Ensemble my senior year of HS. I got downgraded for playing that Ab in 1st..

Well, Konza is part of the University (it's managed by K-State for The Nature Conservancy), so that will work. I hope you're enjoying Ft. Riley.

THIS Tall Grass

https://tallgrasstaphouse.com/

Konza is a great walk though. Beautiful

[tbdana]

Yeah, I played it in Solo/Ensemble my senior year of HS. I got downgraded for playing that Ab in 1st..

Yikes. I would have screamed bloody hell about that. Who the hell is that adjudicator to tell you what position you can and cannot play notes in? If it sounds good and is in tune, it's right. Sounds like that adjudicator needed to take some trombone lessons. Man, I'd have torn that guy a new one and pursued his job.

The orthodoxy of Ab in 1st position is elementary. It's what we teach children and beginners the same way we teach them Bb is in 1st position when they're brand new, and omit that it can be played in a sharp 5th position, too. The Ab can be played in a sharp 1st position (or even in a regular 1st position depending on the horn, if its harmonic function makes it in tune when flat; e.g. the third in a major chord). Clearly that adjudicator never learned anything beyond beginner trombone playing. I'll bet he couldn't tell you whether the note was in tune or not, he just saw it and thought he was being oh-so-insightful and clever when he was actually missing the boat. He probably never learned the very first lesson, which is that 1st position isn't all the way in.

This will ruffle feathers, but IMHO this is a problem with educators who are too often more about orthodoxy and pedantism than about actually playing the trombone. It's what's behind that whole "those who can, do" thing.

I'd have been, "C'mon, mofo, break out your horn and let's see if you can keep up." Sheesh. I think you can tell that story pissed me off. Let me at him! LOL!

[Dennis]

THIS Tall Grass

https://tallgrasstaphouse.com/

Konza is a great walk though. Beautiful

One of these days I'll get back to Riley County/Manhattan, and that Tallgrass is on my list of places to go.

I'll return the favor: if you're ever in Santa Fe, the Blue Corn Cafe/Hidden Mountain Brewing on Cerrillos is not to be missed.

[cmccain]

This will ruffle feathers, but IMHO this is a problem with educators who are too often more about orthodoxy and pedantism than about actually playing the trombone. It's what's behind that whole "those who can, do" thing.

I'd have been, "C'mon, mofo, break out your horn and let's see if you can keep up." Sheesh. I think you can tell that story pissed me off. Let me at him! LOL!

Coming from the education world, I'll take it one further: many higher-ups in education (both secondary and post-secondary) are highly prone to hiring and promoting the orthodox and the pedantic. Too often, hiring and promotion decisions are made by individuals with no experience in the field, without proper consultation and humility, which initiates a vicious feedback loop between pedantic educator and orthodox administrator.

This certainly does not always happen, but it is a nasty, pernicious tendency in (at least American) education that spreads far beyond music education. There are a lot of great educators and administrators out there, most of whom have plenty of stories of individuals getting hired, promoted, or given awards for being the MOST pedantic, ultra orthodox, rule-policing go-getters. I have unfortunately known more than one friend leave education because they made too much noise about the shortcomings of educational orthodoxy.

[Dennis]

Yikes. I would have screamed bloody hell about that. Who the hell is that adjudicator to tell you what position you can and cannot play notes in? If it sounds good and is in tune, it's right. Sounds like that adjudicator needed to take some trombone lessons. Man, I'd have torn that guy a new one and pursued his job.

The orthodoxy of Ab in 1st position is elementary. It's what we teach children and beginners the same way we teach them Bb is in 1st position when they're brand new, and omit that it can be played in a sharp 5th position, too. The Ab can be played in a sharp 1st position (or even in a regular 1st position depending on the horn, if its harmonic function makes it in tune when flat; e.g. the third in a major chord). Clearly that adjudicator never learned anything beyond beginner trombone playing. I'll bet he couldn't tell you whether the note was in tune or not, he just saw it and thought he was being oh-so-insightful and clever when he was actually missing the boat. He probably never learned the very first lesson, which is that 1st position isn't all the way in.

I'd have been, "C'mon, mofo, break out your horn and let's see if you can keep up." Sheesh. I think you can tell that story pissed me off. Let me at him! LOL!

That was decades ago. I'm not even sure the woman was a trombonist, so yeah, it wouldn't suprise me if her total experience with the trombone was a couple of weeks in a brass methods class. The passage in question is a descending Eb7 arpeggio in 16ths at q = 118. The scalar/harmonic function of the Ab is 7th: this passage was made for the first position Ab in that sense. (And yes, I'd learned enough theory by that time to know those things.) I can't say that I wasn't warned ahead of time by my teacher: he suggested the high Bb and Ab in 3rd sequencing. The horn I was playing at the time (Conn 72H with a Bach 1 1/2 G that I played about 1/4 inch off the springs for 1st) didn't have a particularly good high Bb in 3rd, so I chose to do it my way. (My graduation gift from my parents was a Bach 36B I still own, and it has a better high Bb in 3rd than in 1st, but it was several months in the future for me due to Bach's production schedules.)

Taking on an adult like that would be a lot to ask of 17 year old me. All told, it was a valuable lesson--my first lesson that too many people listen with their eyes rather than their ears. It wasn't the last such lesson: I caught some crap in college and grad school about the Bach 36, but even then I preferred the 36 to the 42. Maybe if Bach had made the 36 to use a large-shank mouthpiece...

[OneTon]

Adjudicator?

I will say hi to K-State for you, but only from within the confines of Tall Grass!

Yeah, I played it in Solo/Ensemble my senior year of HS. I got downgraded for playing that Ab in 1st..

Well, Konza is part of the University (it's managed by K-State for The Nature Conservancy), so that will work. I hope you're enjoying Ft. Riley.

I worked a door to the performance room at a state level competition in Newton, KS, for several years. Most of the adjudicators were competent. Occasionally one of them would not get asked to come back. A few of them were back year after year. People who are pedantic, narrow minded, or poorly trained may tend to gather like schools of fish. Most of the time they are fortunately in a small and lonely minority, in my experience. It is never endearing to run into one of them. If I told Herb Rankin about a negative experience, he would make a joke and we would continue with the lesson. I hope Fort Riley is quieter than McConnel AFB. I have Blue Angel F-18 Hornets flying over my house in afterburner. Time to go get the ear plugs.

[Dennis]

Ft. Riley has helicopters--Chinooks, Apaches, Blackhawks, etc. They're noisy, but nothing like a Super Hornet on afterburner.

I worked for a couple of years at KDHE's offices on the old Forbes AFB, and I remember the noise when the Navy was flying their jets in to get away from hurricanes in Florida.

[dukesboneman]

I play with my tuning slide all the way in. I`ve been playing that way since 1975.
I have a useable Ab in 1st but, I use mostly 3rd position just out of habit and having it drilled into my head as a
young player that you don`t use 1st.
I use the 1st position Ab more as a phrasing option or for a slightly different color

[imsevimse]

He probably never learned the very first lesson, which is that 1st position isn't all the way in.

I do not tune Bb all the way in against the bumpers either but have learned here that many players do because they have short arms. If you have short arms and play "long positions" you may not be able to play a B on seventh.

I tune in a way I can play D in first. This means pretty long positions but not impossible to play B on 7:th. I do reach a B on seventh If I have the time to streach the arm and push the right shoulder forward. I can not play an intune Ab on first. To do that I would need to tune even sharper but my tuningslide is already in a closed position so can not see how this will be possible unless I shorten my tuningslide.

[Doldom]

Ab in 1st position is out of tune in the context of 12 tone equal temperament, which is actually pretty out of tune in the context of just intonated harmony.
Ab is 7th harmonic series of a brass instrument and it unlocks septimal intervals(frequency ratio consists of 7, like 7:6 or 7:5 or 7:4) and I think it's unfortunate to abandon these intervals in modern music theory. If you listen to subminor triad(6:7:9) or dominant seventh chord(4:5:6:7) , that chords are one of most beautiful chords.!

I don't have exposure to any German trombones, but, are they really have in-tune Ab in first position (for 12 tone equal temperament)? I thought any instrument should have naturally 30cents low 7th harmonic note, but, if it have in tune note for 12-tet, then maybe the design is flawed and that flawed design somehow contribute to the difficultness and demise of the German trombone?

[harrisonreed]

Ab in 1st position is out of tune in the context of 12 tone equal temperament, which is actually pretty out of tune in the context of just intonated harmony.

This is not true unless your trombone is not capable of being tuned high enough. Most bones in my experience allow for an in tune Ab in 1st. Technically, if you're pushed in all the way you should have an Ab that is in tune on the bumpers for many, maybe even most, trombones.

[Burgerbob]

Every horn is different, very few of them are exactly 30 cents low compared to the Bb.

[LeTromboniste]

Ab in 1st position is out of tune in the context of 12 tone equal temperament, which is actually pretty out of tune in the context of just intonated harmony.
Ab is 7th harmonic series of a brass instrument and it unlocks septimal intervals(frequency ratio consists of 7, like 7:6 or 7:5 or 7:4) and I think it's unfortunate to abandon these intervals in modern music theory. If you listen to subminor triad(6:7:9) or dominant seventh chord(4:5:6:7) , that chords are one of most beautiful chords.!

I don't have exposure to any German trombones, but, are they really have in-tune Ab in first position (for 12 tone equal temperament)? I thought any instrument should have naturally 30cents low 7th harmonic note, but, if it have in tune note for 12-tet, then maybe the design is flawed and that flawed design somehow contribute to the difficultness and demise of the German trombone?

I'm not a fan of equal temperament (although realistically, we rarely actually play in equal temperament anyway). But I'd just point out that the 7:4 "harmonic" seventh is extremely foreign to most Western tuning systems. Even in 5-limit just intonation, you still often don't have that pure seventh, instead you often have the minor seventh tuned to the 5th rather than the root, which is even higher than an equal-tempered minor 7th. And a chord formed of a pure major third, pure fifth and harmonic seventh, which is a very beautiful chord, is not a dominant seventh chord – it lacks all the tension that the tonal language requires a dominant chord to have.

And for German trombones, that partial does tend to be somewhat higher, but most importantly those instruments have long spring in the barrels, so you can push in. They also historically didn't have tuning slides, so 1st position was never all the way in. The fact that an equal temperament Ab (or higher) can be played in 1st would be an advantage, not an inconvenient. Ab needs to be raised way more often than it needs to be lowered (and you can always lower it if the slide if you need)

[tbdana]

Ab in 1st position is out of tune in the context of 12 tone equal temperament, which is actually pretty out of tune in the context of just intonated harmony.
Ab is 7th harmonic series of a brass instrument and it unlocks septimal intervals(frequency ratio consists of 7, like 7:6 or 7:5 or 7:4) and I think it's unfortunate to abandon these intervals in modern music theory. If you listen to subminor triad(6:7:9) or dominant seventh chord(4:5:6:7) , that chords are one of most beautiful chords.!

I don't have exposure to any German trombones, but, are they really have in-tune Ab in first position (for 12 tone equal temperament)? I thought any instrument should have naturally 30cents low 7th harmonic note, but, if it have in tune note for 12-tet, then maybe the design is flawed and that flawed design somehow contribute to the difficultness and demise of the German trombone?

No offense, but to my practical, uneducated mind, just play in tune with notes are only out of tune if you play them out of tune.

[tbdana]

Ab in 1st position is out of tune in the context of 12 tone equal temperament, which is actually pretty out of tune in the context of just intonated harmony.
Ab is 7th harmonic series of a brass instrument and it unlocks septimal intervals(frequency ratio consists of 7, like 7:6 or 7:5 or 7:4) and I think it's unfortunate to abandon these intervals in modern music theory. If you listen to subminor triad(6:7:9) or dominant seventh chord(4:5:6:7) , that chords are one of most beautiful chords.!

I don't have exposure to any German trombones, but, are they really have in-tune Ab in first position (for 12 tone equal temperament)? I thought any instrument should have naturally 30cents low 7th harmonic note, but, if it have in tune note for 12-tet, then maybe the design is flawed and that flawed design somehow contribute to the difficultness and demise of the German trombone?

No offense, but to my practical, uneducated mind, this sounds like nonsense. We can just play in tune. Notes are only out of tune if you play them out of tune.

[LeTromboniste]

Ab in 1st position is out of tune in the context of 12 tone equal temperament, which is actually pretty out of tune in the context of just intonated harmony.
Ab is 7th harmonic series of a brass instrument and it unlocks septimal intervals(frequency ratio consists of 7, like 7:6 or 7:5 or 7:4) and I think it's unfortunate to abandon these intervals in modern music theory. If you listen to subminor triad(6:7:9) or dominant seventh chord(4:5:6:7) , that chords are one of most beautiful chords.!

I don't have exposure to any German trombones, but, are they really have in-tune Ab in first position (for 12 tone equal temperament)? I thought any instrument should have naturally 30cents low 7th harmonic note, but, if it have in tune note for 12-tet, then maybe the design is flawed and that flawed design somehow contribute to the difficultness and demise of the German trombone?

No offense, but to my practical, uneducated mind, this sounds like nonsense. We can just play in tune. Notes are only out of tune if you play them out of tune.

One of the problems is, there's more than one definition of "in tune" for the seventh of a chord, and they go in drastically opposite directions, like, a quarter-tone apart

[tbdana]

One of the problems is, there's more than one definition of "in tune" for the seventh of a chord, and they go in drastically opposite directions, like, a quarter-tone apart

I didn’t go to music conservatory. I’m just a player who has been lucky enough to play with some of the best musicians in the world. So I don’t know about all these definitions of in-tune. To me, either a note is in-tune when I play it or it’s not. There are no definitions, arguments or positions. It’s either in-tune or it isn’t. And if it isn’t, you adjust until it is.

Personally, if you’re playing a note and you say to yourself, well, it’s in-tune under a particular definition even though it sounds out of tune, it’s freaking out of tune. Period. But that’s just me. I guess you can think of me as a just intonation proponent. I play music, I don’t live in a rarified academic world where a note can be both in and out of tune at the same time. There are no Schroedinger’s notes in my world.

[LeTromboniste]

One of the problems is, there's more than one definition of "in tune" for the seventh of a chord, and they go in drastically opposite directions, like, a quarter-tone apart

I didn’t go to music conservatory. I’m just a player who has been lucky enough to play with some of the best musicians in the world. So I don’t know about all these definitions of in-tune. To me, either a note is in-tune when I play it or it’s not. There are no definitions, arguments or positions. It’s either in-tune or it isn’t. And if it isn’t, you adjust until it is.

Personally, if you’re playing a note and you say to yourself, well, it’s in-tune under a particular definition even though it sounds out of tune, it’s freaking out of tune. Period. But that’s just me. I guess you can think of me as a just intonation proponent. I play music, I don’t live in a rarified academic world where a note can be both in and out of tune at the same time. There are no Schroedinger’s notes in my world.

I know you dislike these kinds of discussions but please bear with me. Ok, so "in tune" means the note you play and its overtones are lining up with other notes played at the same time and their overtones, surely we all agree on that. You have a Bb chord, your F or D is in tune if it matches the F or D that's within the Bb's overtones. This is easy because they are the first overtones of Bb that are not simply other octaves of Bb, they are are very prominent in the harmonic make-up of the root. So those notes just lock in very well.

The problem with the minor 7th is that it's a remote and weak harmonic relationship, and depending on the chord, it will be much more closely related to various other notes of the chord than it is to the root.

One can tune it so that it matches perfectly that overtone of the root, then you have to lower it by a ridiculous amount. It's so low that we can't even technically call it a "minor 7th" anymore, instead it's a "harmonic" or "subminor" 7th. It's a "blue note". It's a beautiful, in-tune sound. Barbershop quartets singing with pure 7ths is absolutely glorious. But in most contexts, and particularly on instruments, we very rarely, if ever at all, lower it by anywhere near that much.

There's another perfectly valid way of tuning the same note in the same harmonic context. Let's assume a Bb dominant 7th chord. Ab and F, both notes being played within the chord, are much more closely related than Ab and Bb are: for one, they are consonant, and they share a very prominent overtone, C (which is also a higher overtone of Bb). When you tune that Ab so low that it's "pure" to the Bb, all those C overtones are completely out of whack with each other, and the F and Ab are no longer consonant together. Now let's assume it's a minor 7th instead of a dominant 7th chord. The Db and Ab form a perfect fifth, which is the closest relation there is. If your Ab is in tune with the the Ab in the Bb's overtone, it will be completely off from the much more prominent Ab in the Db's overtones in addition to being off from the F. This is why a lot of people will raise, not lower, their minor 7ths, and tune them as a pure minor third above the 5th, or as a pure perfect fifth above the minor 3rd.

The difference between the lowered "harmonic 7th" version and the raised "in-tune with the 5th of the chord" version is a quarter tone! But which one is "in tune"? Either of these ways to tune it requires a compromise. Either you line up with the overtones of the root but not with the other notes of the chord, or the opposite, but you simply cannot ever do both at the same time. Both versions do sound in tune, but the resulting feel of the chord is vastly different.

[tbdana]

I know you dislike these kinds of discussions but please bear with me. Ok, so "in tune" means the note you play and its overtones are lining up with other notes played at the same time and their overtones, surely we all agree on that. You have a Bb chord, your F or D is in tune if it matches the F or D that's within the Bb's overtones. This is easy because they are the first overtones of Bb that are not simply other octaves of Bb, they are are very prominent in the harmonic make-up of the root. So those notes just lock in very well.

The problem with the minor 7th is that it's a remote and weak harmonic relationship, and depending on the chord, it will be much more closely related to various other notes of the chord than it is to the root.

One can tune it so that it matches perfectly that overtone of the root, then you have to lower it by a ridiculous amount. It's so low that we can't even technically call it a "minor 7th" anymore, instead it's a "harmonic" or "subminor" 7th. It's a "blue note". It's a beautiful, in-tune sound. Barbershop quartets singing with pure 7ths is absolutely glorious. But in most contexts, and particularly on instruments, we very rarely, if ever at all, lower it by anywhere near that much.

There's another perfectly valid way of tuning the same note in the same harmonic context. Let's assume a Bb dominant 7th chord. Ab and F, both notes being played within the chord, are much more closely related than Ab and Bb are: for one, they are consonant, and they share a very prominent overtone, C (which is also a higher overtone of Bb). When you tune that Ab so low that it's "pure" to the Bb, all those C overtones are completely out of whack with each other, and the F and Ab are no longer consonant together. Now let's assume it's a minor 7th instead of a dominant 7th chord. The Db and Ab form a perfect fifth, which is the closest relation there is. If your Ab is in tune with the the Ab in the Bb's overtone, it will be completely off from the much more prominent Ab in the Db's overtones in addition to being off from the F. This is why a lot of people will raise, not lower, their minor 7ths, and tune them as a pure minor third above the 5th, or as a pure perfect fifth above the minor 3rd.

The difference between the lowered "harmonic 7th" version and the raised "in-tune with the 5th of the chord" version is a quarter tone! But which one is "in tune"? Either of these ways to tune it requires a compromise. Either you line up with the overtones of the root but not with the other notes of the chord, or the opposite, but you simply cannot ever do both at the same time. Both versions do sound in tune, but the resulting feel of the chord is vastly different.

Okay. I hear all that. And I think all that knowledge is very impressive. It's dizzying to think about.

But I can't get into it. I guess I'm just a little simple-minded. When I come to that half note, I just play it so it sounds in tune and "right." With respect to applying your last paragraph to a half note I come across 7 bars into a phrase, for me there's no utility to it. It's a half note; I'm not going to analyze it. By the time I recognize what kind of chord it is, what function in the chord my note has, whether I should play it as a harmonic 7th or in tune with the 5th of the chord, and which overtones I want to line up with, it's already gone and I'm on to another note.

In my simple-minded way of thinking...I don't think. I hear. I hear that half note, and the note before it, and where it's going, and I just play what sounds in-tune and correct. I don't have time for academic pursuits. I don't have time to make decisions. Both my brain cells are just trying to read ahead a few bars so I play whatever's in front of me well. I only have time to listen and place my notes where they sound in-tune and right to the ear. And one note means very little to me. I'm too busy trying to make some music, and I just listen and feel, and I've gotten very good at putting notes where they sound right.

And the weird thing is that I've never once in 50 years felt there were multiple choices for my in-tune note. I've always felt there was one slot for it, and only one slot. I know when I hit that slot and when I miss it. And yeah, I've made exceptions for interpretation, such as playing a "blue note." But it's not something I consciously consider. I just hear it and try to play what I hear, and sometimes it doesn't even have to be in-tune.

You guys who analyze which "in-tune" between multiple "in-tune" choices you're going for on any particular note, either as an academic exercise or as the notes fly by, must be geniuses compared to me. That's all beyond my capability. I didn't have a big music education. And I simply don't think when I play. I can't think when I play. If I do, it destroys the music. I just listen and play and feel; and play in-tune. I know when it sounds right, and I know when it sounds wrong. That's as much analysis as I can handle with my two functioning brain cells. I can't find the practicality in trying to analyze all the different theories of in-tune there are in the conceptual universe. I'm not tuning pianos or anything where I have to make compromises or work within certain inherent limits. I'm just playing whatever piece has been put in front of me. In my barely working brain, I figure that if you have big ears you just know when it sounds right. Play it where it sounds right. I'll leave the splitting of hairs and dancings on head of pins to you brainiacs.

Oops. Now that half-note is long gone, and I'm four bars behind because I've been thinking about which kind of in-tune I'm going to play.

:shrug: Don't be mad or disappointed. I'm just wired differently.

And I've completely lost how this connects to playing Ab in 1st position.

[harrisonreed]

It also depends on the genre though. In some genres of music, you DO NOT adjust for those chords. Especially in a jazz combo when you have the pianist right next to you giving you the chords.

In orchestral music, when you have only 8 notes, you can analyze the crap out of it, and hopefully everyone else plays the chord all friendly with you. But even in the orchestra, the 7th might act completely differently if it is serving a melodic, rather than harmonic, function.

In 12TET, at the very least, you can play that Ab in 1st no prob.

[BGuttman]

The time to analyze where the Ab in 1sr should be or not be is in the practice room. Even dedicated sight readers need to practice fundamentals so that they know what will come out when they play.

There are some horns with a useable Ab in 1st position. I don't own any. However, I can get a short Ab in 1st that will serve as a passing tone. But for years I have trained myself not to trust it.

[Doldom]

Yes, you can play any note in tune because we have biggest tuning mechanism, "the slide"
Yes, I also agree that, with the tuning slide in, some instrument can produce viable 12-tet in tune Ab in first position.
I just wanted to say that, the "out of tune" Ab note is not just an oddball or flaw of the instrument, but because of the physics, standing wave of 7th harmonic note of an open-end tube is very flat by its nature.
But again, I searched web a little and discover that the physics of brass instrument is far more complicated than the physics of sound production of just the "open-end" or "closed-end" tube.
But even so, I think brass instrument generally follows the tendency of harmonic series. 3rd harmonic(F in the middle) is naturally a little sharp and 7th harmonic(Ab) is very flat. 6th harmonic(F) is sharp, too. But again, 5th harmonic(D) is supposed to be flat in harmonic series, but I've encountered trombones that has in tune D or even sharp D in first position.
Is there any brass instrument that completely follows the intonation tendency of natural harmonic series? Is it possible to even manufacture one? Maybe some instrument maker have an answer.

My post seems a little bit rabbit hole. I completely agree that Ab in 1st position is absolutely usable in certain situations.

[Doldom]

The difference between the lowered "harmonic 7th" version and the raised "in-tune with the 5th of the chord" version is a quarter tone! But which one is "in tune"? Either of these ways to tune it requires a compromise. Either you line up with the overtones of the root but not with the other notes of the chord, or the opposite, but you simply cannot ever do both at the same time. Both versions do sound in tune, but the resulting feel of the chord is vastly different.

And the weird thing is that I've never once in 50 years felt there were multiple choices for my in-tune note. I've always felt there was one slot for it, and only one slot. I know when I hit that slot and when I miss it. And yeah, I've made exceptions for interpretation, such as playing a "blue note." But it's not something I consciously consider. I just hear it and try to play what I hear, and sometimes it doesn't even have to be in-tune.

I think he is referring to this.
There's many "in-tune" tunings of 7th, as shown in this video.
I think quarter tone difference means this. the lowest possible tuning is 968 cents(which is, the 4:5:6:7 chord I mentioned earlier), and the highest possible tuning is 1017 cents. so there's a 49 cents difference.


But again, there is no absolute "consonance" or "dissonance" and all the tuning has compromises as he said.
But some tuning seems friendly, because, our ears are so accustomed to 12-tet music.
I mentioned subminor triad(6:7:9) and, If someone construct a chord using 6th harmonic(F above the staff), 7th harmonic (flat Ab above the staff, no alteration of position), 9th harmonic (High C), it will become F subminor triad, and it will sound a little alien, yet very beautiful.

This is although 31-tet video clip, but 31-tet is a very nice approximation of just intonation, and it shows the subminor triad very nicely. I almost feels the subminor triad (6:7:9) more consonant than normal minor triad (10:12:15). maybe because it consists smaller number of integers.


But again, I mentioned this because of physical nature of the 7th harmonic, not an intent to bring it to a rabbit hole.

[LeTromboniste]

Okay. I hear all that. And I think all that knowledge is very impressive. It's dizzying to think about.

But I can't get into it. I guess I'm just a little simple-minded. When I come to that half note, I just play it so it sounds in tune and "right." With respect to applying your last paragraph to a half note I come across 7 bars into a phrase, for me there's no utility to it. It's a half note; I'm not going to analyze it. By the time I recognize what kind of chord it is, what function in the chord my note has, whether I should play it as a harmonic 7th or in tune with the 5th of the chord, and which overtones I want to line up with, it's already gone and I'm on to another note.

In my simple-minded way of thinking...I don't think. I hear. I hear that half note, and the note before it, and where it's going, and I just play what sounds in-tune and correct. I don't have time for academic pursuits. I don't have time to make decisions. Both my brain cells are just trying to read ahead a few bars so I play whatever's in front of me well. I only have time to listen and place my notes where they sound in-tune and right to the ear. And one note means very little to me. I'm too busy trying to make some music, and I just listen and feel, and I've gotten very good at putting notes where they sound right.

And the weird thing is that I've never once in 50 years felt there were multiple choices for my in-tune note. I've always felt there was one slot for it, and only one slot. I know when I hit that slot and when I miss it. And yeah, I've made exceptions for interpretation, such as playing a "blue note." But it's not something I consciously consider. I just hear it and try to play what I hear, and sometimes it doesn't even have to be in-tune.

You guys who analyze which "in-tune" between multiple "in-tune" choices you're going for on any particular note, either as an academic exercise or as the notes fly by, must be geniuses compared to me. That's all beyond my capability. I didn't have a big music education. And I simply don't think when I play. I can't think when I play. If I do, it destroys the music. I just listen and play and feel; and play in-tune. I know when it sounds right, and I know when it sounds wrong. That's as much analysis as I can handle with my two functioning brain cells. I can't find the practicality in trying to analyze all the different theories of in-tune there are in the conceptual universe. I'm not tuning pianos or anything where I have to make compromises or work within certain inherent limits. I'm just playing whatever piece has been put in front of me. In my barely working brain, I figure that if you have big ears you just know when it sounds right. Play it where it sounds right. I'll leave the splitting of hairs and dancings on head of pins to you brainiacs.

Oops. Now that half-note is long gone, and I'm four bars behind because I've been thinking about which kind of in-tune I'm going to play.

:shrug: Don't be mad or disappointed. I'm just wired differently.

Just to be clear, nobody is doing this long analysis in real time – it was just a demonstration about one issue with saying "just play in tune", that for comlex intervals there's more that one "in tune" – and also not typically doing it in advance/in the practice room either. I personally don't have to do much of any of that at all anymore because I play in fixed tuning systems that sound good without needing huge adjustments, but, overall, classical/orchestral players develop, very early-on, the awareness of what note of the chord they are on at any given time, and an understanding of voice-leading that allows one to predict it on-the-fly without actually thinking much about. It eventually becomes automatic. They very, very much play every note in several different places depending on the chords, that's the only way to play in tune as a section. Major thirds need to be played very low, minor thirds very high, etc. That's just an acoustic reality, and that's one of the most basic skills for that style of work, and something you learn week 1 of studying in that field. Playing chords really in tune is kind of the bread and butter of the orchestral trombonist.

You say there's no time to think, but there's also no time to fish around and find out if your note has to be lowered or raised. One can't think and one can't try either, so one needs to know.

I think we're really just saying the same thing, but it sounds to me like you know purely instinctively, without having ever had to give it any thought at all, and in that case I would say you're the genius, not those of us who actually had to learn it and always have to waste some portion of our brainpower to doing it!

And I've completely lost how this connects to playing Ab in 1st position.

It doesn't, but also it does a little. On some horns, and if you tune with your 1st position far enough from the bumpers, you can indeed play Ab in 1 in most situations. But there will still be some harmonic contexts where you can't get it high enough to be in tune. I've never played any instrument where you can play your Ab in tune in 1st when the group is playing an F minor chord, for instance.

[Kdanielsen]

I know you dislike these kinds of discussions but please bear with me. Ok, so "in tune" means the note you play and its overtones are lining up with other notes played at the same time and their overtones, surely we all agree on that. You have a Bb chord, your F or D is in tune if it matches the F or D that's within the Bb's overtones. This is easy because they are the first overtones of Bb that are not simply other octaves of Bb, they are are very prominent in the harmonic make-up of the root. So those notes just lock in very well.

The problem with the minor 7th is that it's a remote and weak harmonic relationship, and depending on the chord, it will be much more closely related to various other notes of the chord than it is to the root.

One can tune it so that it matches perfectly that overtone of the root, then you have to lower it by a ridiculous amount. It's so low that we can't even technically call it a "minor 7th" anymore, instead it's a "harmonic" or "subminor" 7th. It's a "blue note". It's a beautiful, in-tune sound. Barbershop quartets singing with pure 7ths is absolutely glorious. But in most contexts, and particularly on instruments, we very rarely, if ever at all, lower it by anywhere near that much.

There's another perfectly valid way of tuning the same note in the same harmonic context. Let's assume a Bb dominant 7th chord. Ab and F, both notes being played within the chord, are much more closely related than Ab and Bb are: for one, they are consonant, and they share a very prominent overtone, C (which is also a higher overtone of Bb). When you tune that Ab so low that it's "pure" to the Bb, all those C overtones are completely out of whack with each other, and the F and Ab are no longer consonant together. Now let's assume it's a minor 7th instead of a dominant 7th chord. The Db and Ab form a perfect fifth, which is the closest relation there is. If your Ab is in tune with the the Ab in the Bb's overtone, it will be completely off from the much more prominent Ab in the Db's overtones in addition to being off from the F. This is why a lot of people will raise, not lower, their minor 7ths, and tune them as a pure minor third above the 5th, or as a pure perfect fifth above the minor 3rd.

The difference between the lowered "harmonic 7th" version and the raised "in-tune with the 5th of the chord" version is a quarter tone! But which one is "in tune"? Either of these ways to tune it requires a compromise. Either you line up with the overtones of the root but not with the other notes of the chord, or the opposite, but you simply cannot ever do both at the same time. Both versions do sound in tune, but the resulting feel of the chord is vastly different.

Okay. I hear all that. And I think all that knowledge is very impressive. It's dizzying to think about.

But I can't get into it. I guess I'm just a little simple-minded. When I come to that half note, I just play it so it sounds in tune and "right." With respect to applying your last paragraph to a half note I come across 7 bars into a phrase, for me there's no utility to it. It's a half note; I'm not going to analyze it. By the time I recognize what kind of chord it is, what function in the chord my note has, whether I should play it as a harmonic 7th or in tune with the 5th of the chord, and which overtones I want to line up with, it's already gone and I'm on to another note.

In my simple-minded way of thinking...I don't think. I hear. I hear that half note, and the note before it, and where it's going, and I just play what sounds in-tune and correct. I don't have time for academic pursuits. I don't have time to make decisions. Both my brain cells are just trying to read ahead a few bars so I play whatever's in front of me well. I only have time to listen and place my notes where they sound in-tune and right to the ear. And one note means very little to me. I'm too busy trying to make some music, and I just listen and feel, and I've gotten very good at putting notes where they sound right.

And the weird thing is that I've never once in 50 years felt there were multiple choices for my in-tune note. I've always felt there was one slot for it, and only one slot. I know when I hit that slot and when I miss it. And yeah, I've made exceptions for interpretation, such as playing a "blue note." But it's not something I consciously consider. I just hear it and try to play what I hear, and sometimes it doesn't even have to be in-tune.

You guys who analyze which "in-tune" between multiple "in-tune" choices you're going for on any particular note, either as an academic exercise or as the notes fly by, must be geniuses compared to me. That's all beyond my capability. I didn't have a big music education. And I simply don't think when I play. I can't think when I play. If I do, it destroys the music. I just listen and play and feel; and play in-tune. I know when it sounds right, and I know when it sounds wrong. That's as much analysis as I can handle with my two functioning brain cells. I can't find the practicality in trying to analyze all the different theories of in-tune there are in the conceptual universe. I'm not tuning pianos or anything where I have to make compromises or work within certain inherent limits. I'm just playing whatever piece has been put in front of me. In my barely working brain, I figure that if you have big ears you just know when it sounds right. Play it where it sounds right. I'll leave the splitting of hairs and dancings on head of pins to you brainiacs.

Oops. Now that half-note is long gone, and I'm four bars behind because I've been thinking about which kind of in-tune I'm going to play.

:shrug: Don't be mad or disappointed. I'm just wired differently.

And I've completely lost how this connects to playing Ab in 1st position.

Using a Bb minor 7th chord as an example, one issue is that if you play your m7th 30c flat, whoever is playing the Db minor third will never feel locked in because the Ab overtone in their sound is clashing with your 30c flat Ab. It’s uncomfortable to be in the situation where you can’t lock in but nothing helps. It’s always a compromise. I think these things are worth thinking about. First you know them with intellect, later they become intuition.

[Kdanielsen]

I know you dislike these kinds of discussions but please bear with me. Ok, so "in tune" means the note you play and its overtones are lining up with other notes played at the same time and their overtones, surely we all agree on that. You have a Bb chord, your F or D is in tune if it matches the F or D that's within the Bb's overtones. This is easy because they are the first overtones of Bb that are not simply other octaves of Bb, they are are very prominent in the harmonic make-up of the root. So those notes just lock in very well.

The problem with the minor 7th is that it's a remote and weak harmonic relationship, and depending on the chord, it will be much more closely related to various other notes of the chord than it is to the root.

One can tune it so that it matches perfectly that overtone of the root, then you have to lower it by a ridiculous amount. It's so low that we can't even technically call it a "minor 7th" anymore, instead it's a "harmonic" or "subminor" 7th. It's a "blue note". It's a beautiful, in-tune sound. Barbershop quartets singing with pure 7ths is absolutely glorious. But in most contexts, and particularly on instruments, we very rarely, if ever at all, lower it by anywhere near that much.

There's another perfectly valid way of tuning the same note in the same harmonic context. Let's assume a Bb dominant 7th chord. Ab and F, both notes being played within the chord, are much more closely related than Ab and Bb are: for one, they are consonant, and they share a very prominent overtone, C (which is also a higher overtone of Bb). When you tune that Ab so low that it's "pure" to the Bb, all those C overtones are completely out of whack with each other, and the F and Ab are no longer consonant together. Now let's assume it's a minor 7th instead of a dominant 7th chord. The Db and Ab form a perfect fifth, which is the closest relation there is. If your Ab is in tune with the the Ab in the Bb's overtone, it will be completely off from the much more prominent Ab in the Db's overtones in addition to being off from the F. This is why a lot of people will raise, not lower, their minor 7ths, and tune them as a pure minor third above the 5th, or as a pure perfect fifth above the minor 3rd.

The difference between the lowered "harmonic 7th" version and the raised "in-tune with the 5th of the chord" version is a quarter tone! But which one is "in tune"? Either of these ways to tune it requires a compromise. Either you line up with the overtones of the root but not with the other notes of the chord, or the opposite, but you simply cannot ever do both at the same time. Both versions do sound in tune, but the resulting feel of the chord is vastly different.

Okay. I hear all that. And I think all that knowledge is very impressive. It's dizzying to think about.

But I can't get into it. I guess I'm just a little simple-minded. When I come to that half note, I just play it so it sounds in tune and "right." With respect to applying your last paragraph to a half note I come across 7 bars into a phrase, for me there's no utility to it. It's a half note; I'm not going to analyze it. By the time I recognize what kind of chord it is, what function in the chord my note has, whether I should play it as a harmonic 7th or in tune with the 5th of the chord, and which overtones I want to line up with, it's already gone and I'm on to another note.

In my simple-minded way of thinking...I don't think. I hear. I hear that half note, and the note before it, and where it's going, and I just play what sounds in-tune and correct. I don't have time for academic pursuits. I don't have time to make decisions. Both my brain cells are just trying to read ahead a few bars so I play whatever's in front of me well. I only have time to listen and place my notes where they sound in-tune and right to the ear. And one note means very little to me. I'm too busy trying to make some music, and I just listen and feel, and I've gotten very good at putting notes where they sound right.

And the weird thing is that I've never once in 50 years felt there were multiple choices for my in-tune note. I've always felt there was one slot for it, and only one slot. I know when I hit that slot and when I miss it. And yeah, I've made exceptions for interpretation, such as playing a "blue note." But it's not something I consciously consider. I just hear it and try to play what I hear, and sometimes it doesn't even have to be in-tune.

You guys who analyze which "in-tune" between multiple "in-tune" choices you're going for on any particular note, either as an academic exercise or as the notes fly by, must be geniuses compared to me. That's all beyond my capability. I didn't have a big music education. And I simply don't think when I play. I can't think when I play. If I do, it destroys the music. I just listen and play and feel; and play in-tune. I know when it sounds right, and I know when it sounds wrong. That's as much analysis as I can handle with my two functioning brain cells. I can't find the practicality in trying to analyze all the different theories of in-tune there are in the conceptual universe. I'm not tuning pianos or anything where I have to make compromises or work within certain inherent limits. I'm just playing whatever piece has been put in front of me. In my barely working brain, I figure that if you have big ears you just know when it sounds right. Play it where it sounds right. I'll leave the splitting of hairs and dancings on head of pins to you brainiacs.

Oops. Now that half-note is long gone, and I'm four bars behind because I've been thinking about which kind of in-tune I'm going to play.

:shrug: Don't be mad or disappointed. I'm just wired differently.

And I've completely lost how this connects to playing Ab in 1st position.

Using a Bb minor 7th chord as an example, one issue is that if you play your m7th 30c flat, whoever is playing the Db minor third will never feel locked in because the Ab overtone in their sound is clashing with your 30c flat Ab. It’s uncomfortable to be in the situation where you can’t lock in but nothing helps. It’s always a compromise. I think these things are worth thinking about. First you know them with intellect, later they become intuition.

[baileyman]

Heck, if you're playing something rapid maybe from F Ab Bb no one's going to hear a flat Ab even if it is, but when I play a rapid passage there, I can't hear it flat either. You can do the rapid on #4 3 and 3, less secure, or 1 3 3, but both weirder than 1 1 1. But if you're going to hang on that note, play it in 3 and then snick it which way it wants to go, the way all the notes should be adjusted if you hang on them. Remember how Sam said if you watch a NYC section you'll see them snicking all over the place?

[Wilktone]

I really don’t understand the controversy. If the Ab is in tune on your instrument or the situation is such that the intonation sounds good, fine. On all my horns that note is too flat to play in first, although I sometimes practice exercises where I play it in first.

The “academic” intonation adjustments are much more relevant when you play with strings, choirs, or a trombone ensemble. Jazz groups will tend to play with well tempered intonation, since we’re playing with pianos and other instruments that will be more likely to be tuned accordingly.

And no, it doesn’t mean orchestral trombonists are thinking about what note of the chord and the key center and how they need to adjust the note, they are listening in the moment and playing in tune, just like jazz trombonists do. Thinking about how to adjust intonation accordingly and spending some conscious time practicing it won’t hurt your playing and just might help you play with different groups better.

[Kbiggs]

What David Wilken said. Some recent personal experiences, only as an illustration, not gospel:

1. I recently had the opportunity to borrow a friend’s 36 to play some Mendelssohn. While getting used to it, I adjusted it so the tuning slide was almost all the way in, and the main slide was out about one finger’s width (my usual position). I found that I could play an A-flat in tune in 1st. Tuba Mirum sounded and felt easier. I could even play an A-flat scale. I was pleasantly surprised. I thought that only possible on sacbuts and German-style instruments.

2. I played Tchaikovsky Francesca da Rimini overture/tone poem/fantasy recently. Never played it before. It opens with a series of diminished and diminished/diminished 7th cords, interspersed with the occasional major cord and major/minor 7th cord. It’s very unusual harmony, bordering on non-tonal (no key center) in parts. After some disagreement with other sections about the tuning of the cords during rehearsal, I went through the first score page to analyze the piece and find my place.

While I found my place in the cords, and the rest of the trombone & tuba section sounded pretty good on those cords, the entire orchestra didn’t agree: there were different interpretations of how diminished and diminished/diminished 7th cords should sound.

To me, this illustrated several points, one of them being that even if I’m confident that, on paper, I’m reasonably well in tune for that cord, if I don’t agree with other members of the group, then it’s not in tune. It’s about cooperation, not who is correct: how does it sound is more important.

[tbdana]

As I posted before: My first position isn't all the way in, so I can raise the pitch a little on Ab in 1st position. I play Ab in 1st mostly on passing tones or off-beat notes. In all cases, all the time, I simply listen and play each note so it sounds in tune.

I'm not sure what there is to debate about this.

[Doldom]

To instrument makers, is there a design philosophy that consciously forcing up intonation of 7th partial so it can be used? (with tuning slides pulled in and stick out first positions)
I still think the brass instruments should have 30 cents low 7th partial. I think it's not an oddball partial that should be fixed with design tweaks, but rather it's hidden secret of nature's beauty. It unlocks whole new possibility of septimal intervals, just we don't use that interval in modern music.
If someone has sufficiently long hands and play first position stick out long enough from bumpers and make use of 7th partial Ab and it's in-tune with 12-tet, (and still have viable 7th position E and B), I'm totally fine with it and there is no debate. But, that is possible maybe because, there might some design tweaks exist that is forcing up the 7th partial.

[harrisonreed]

To instrument makers, is there a design philosophy that consciously forcing up intonation of 7th partial so it can be used? (with tuning slides pulled in and stick out first positions)
I still think the brass instruments should have 30 cents low 7th partial.

I am not sure what this means exactly, but if you meant to say that Ab is still not possible in 1st with the tuning slide pushed completely in, you're objectively wrong.

I think it's not an oddball partial that should be fixed with design tweaks, but rather it's hidden secret of nature's beauty. It unlocks whole new possibility of septimal intervals, just we don't use that interval in modern music.
If someone has sufficiently long hands and play first position stick out long enough from bumpers and make use of 7th partial Ab and it's in-tune with 12-tet, (and still have viable 7th position E and B), I'm totally fine with it and there is no debate. But, that is possible maybe because, there might some design tweaks exist that is forcing up the 7th partial.

I don't really know what you're talking about with these septimal intervals, that sounds like some deep 7-limit JI concept, but surely that specific interval's JI tuning would be possible using Ab in 3rd, which can be manipulated as far sharp or flat as you could possibly want. Playing it in 1st doesn't give you any "new" tuning option -- the tuning is much less flexible than in the standard 3rd position.

[Doldom]

To instrument makers, is there a design philosophy that consciously forcing up intonation of 7th partial so it can be used? (with tuning slides pulled in and stick out first positions)
I still think the brass instruments should have 30 cents low 7th partial.

I am not sure what this means exactly, but if you meant to say that Ab is still not possible in 1st with the tuning slide pushed completely in, you're objectively wrong.

I think it's not an oddball partial that should be fixed with design tweaks, but rather it's hidden secret of nature's beauty. It unlocks whole new possibility of septimal intervals, just we don't use that interval in modern music.
If someone has sufficiently long hands and play first position stick out long enough from bumpers and make use of 7th partial Ab and it's in-tune with 12-tet, (and still have viable 7th position E and B), I'm totally fine with it and there is no debate. But, that is possible maybe because, there might some design tweaks exist that is forcing up the 7th partial.

I don't really know what you're talking about with these septimal intervals, that sounds like some deep 7-limit JI concept, but surely that specific interval's JI tuning would be possible using Ab in 3rd, which can be manipulated as far sharp or flat as you could possibly want. Playing it in 1st doesn't give you any "new" tuning option -- the tuning is much less flexible than in the standard 3rd position.

Have you ever wondered why the 7th partial is so low in the first place?
If a trombone is tuned to A=440, then fundamental frequency wound be approximately 58.3 Hz.(this is pedal Bb)
Any partials that is stacked upwards have a frequency that has integer ratio with the fundamental frequency. (Let's assume that a trombone follows "perfect" harmonic series.)
2nd partial = 2*58.3Hz = 116.6Hz (Bb2)
3rd partial = 3*58.3Hz = 174.9Hz (F3)
4th partial = 4*58.3Hz = 233.2Hz (Bb3)
5th partial = 5*58.3Hz = 291.5Hz (D4)
6th partial = 6*58.3Hz = 349.8Hz (F4)
7th partial = 7*58.3Hz = 408.1Hz (Ab4)
8th partial = 8*58.3Hz = 466.4Hz (Bb4)
etc...

But, in equal temperament, F3 is 174.6Hz. D4 is 293.7Hz. F4 is 349.3Hz. Ab4 is 415.4Hz.
There is so much discrepancy at Ab4 note (408Hz vs 415Hz) and it's approximately 31 cents difference.

But, as Aidan said before, there is very few trombones that really have 31cent low 7th partial. (I'm talking about no slide adjustment. If you blow Bb3 in stick-out first position, don't do any slide adjustment and blow Ab at that same position. Let's assume that someone is playing valve trombone or trumpet. It will make this more understandable.) I'll check my trombones again with tuner, But if Aidan is right that many trombones have in fact "not-that-low" 7th partial, there must be some design element that is forcing the intonation of the partial up to that point. So that with the "forced up 7th partial" slide trombone, some can use 12tet Ab in first position, with pushed tuning slides and stick-out first position for other notes. That was the point that I wanted to say.

If a trombone is built with "real 31cent low 7th partial", then, it will be much harder to achieve 12-tet Ab in first position, even if you push the tuning slide all the way in. Even harder, in countries that is using A=442 or 443Hz. That was my point.


And, of course, slide trombone has "The slide" so you can do any interval in any partial whatsoever.
I'm saying that, the "perfect" harmonic series teaches us the hidden interval that we really don't use anymore in modern music.
1st to 2nd partial is an octave. with a frequency ratio of 1:2
2nd to 3rd partial is a perfect fifth. 2:3
3rd to 4th partial is a perfect fourth. 3:4
4th to 5th is a major third. 4:5
5th to 6th is a minor third. 5:6
6th to 7th partial? it's a septimal minor third or subminor third that modern music don't use. 6:7
7th to 8th is septimal major second or supermajor second. 7:8

Assume that someone is playing valve trombone, or trumpet, and, you don't have tuning option for these septimal intervals, except the 7th partial notes, with a very limited note choices.

[LeTromboniste]

I am not sure what this means exactly, but if you meant to say that Ab is still not possible in 1st with the tuning slide pushed completely in, you're objectively wrong.



I don't really know what you're talking about with these septimal intervals, that sounds like some deep 7-limit JI concept, but surely that specific interval's JI tuning would be possible using Ab in 3rd, which can be manipulated as far sharp or flat as you could possibly want. Playing it in 1st doesn't give you any "new" tuning option -- the tuning is much less flexible than in the standard 3rd position.

Have you ever wondered why the 7th partial is so low in the first place?
If a trombone is tuned to A=440, then fundamental frequency wound be approximately 58.3 Hz.(this is pedal Bb)
Any partials that is stacked upwards have a frequency that has integer ratio with the fundamental frequency. (Let's assume that a trombone follows "perfect" harmonic series.)
2nd partial = 2*58.3Hz = 116.6Hz (Bb2)
3rd partial = 3*58.3Hz = 174.9Hz (F3)
4th partial = 4*58.3Hz = 233.2Hz (Bb3)
5th partial = 5*58.3Hz = 291.5Hz (D4)
6th partial = 6*58.3Hz = 349.8Hz (F4)
7th partial = 7*58.3Hz = 408.1Hz (Ab4)
8th partial = 8*58.3Hz = 466.4Hz (Bb4)
etc...

But, in equal temperament, F3 is 174.6Hz. D4 is 293.7Hz. F4 is 349.3Hz. Ab4 is 415.4Hz.
There is so much discrepancy at Ab4 note (408Hz vs 415Hz) and it's approximately 31 cents difference.

But, as Aidan said before, there is very few trombones that really have 31cent low 7th partial. (I'm talking about no slide adjustment. If you blow Bb3 in stick-out first position, don't do any slide adjustment and blow Ab at that same position. Let's assume that someone is playing valve trombone or trumpet. It will make this more understandable.) I'll check my trombones again with tuner, But if Aidan is right that many trombones have in fact "not-that-low" 7th partial, there must be some design element that is forcing the intonation of the partial up to that point. So that with the "forced up 7th partial" slide trombone, some can use 12tet Ab in first position, with pushed tuning slides and stick-out first position for other notes. That was the point that I wanted to say.

If a trombone is built with "real 31cent low 7th partial", then, it will be much harder to achieve 12-tet Ab in first position, even if you push the tuning slide all the way in. Even harder, in countries that is using A=442 or 443Hz. That was my point.


And, of course, slide trombone has "The slide" so you can do any interval in any partial whatsoever.
I'm saying that, the "perfect" harmonic series teaches us the hidden interval that we really don't use anymore in modern music.
1st to 2nd partial is an octave. with a frequency ratio of 1:2
2nd to 3rd partial is a perfect fifth. 2:3
3rd to 4th partial is a perfect fourth. 3:4
4th to 5th is a major third. 4:5
5th to 6th is a minor third. 5:6
6th to 7th partial? it's a septimal minor third or subminor third that modern music don't use. 6:7
7th to 8th is septimal major second or supermajor second. 7:8

Assume that someone is playing valve trombone, or trumpet, and, you don't have tuning option for these septimal intervals, except the 7th partial notes, with a very limited note choices.

We're getting way off the topic of this discussion, and I have a feeling Dana will roll her eyes so far that they'll actually still face forward

But your idea that the trombone partials should match the natural harmonic series is plain wrong. Two basic reasons for that.

1) the trombone is a cylindrical pipe open at one end, and as such theoretically should only resonate on the odd harmonics, and therefore overblow at the 12th. The reason our partials appear to be like a natural harmonic series is that the bell and the mouthpiece combine in squishing the partials together, and overall raising them, approximating a normal harmonic series with all harmonics present. That we can access a harmonic series has nothing natural, it is entirely artificial and the result of the instrument's design and not direct natural properties. There would be nothing inherently more natural in a trombone that has the A 30 cents flat than one that has it playable in 1, because in reality that note is not the 7th harmonic of the pipe you're playing, it's the 15th that's been squished down by about a tritone to sound like the 7th.

2) even if this wasn't the case, and the trombone naturally produced a harmonic series, it still would not match it precisely, because the theoretical model is just that, a theoretical model. It assumes a perfect system, and in this case a tube with an infinitely small diameter. No instrument is a perfect system, all instruments have some degree of inharmonicity, because of the constraints of actually building them as physical objects in the real world.

[harrisonreed]

Have you ever wondered why the 7th partial is so low in the first place?

Briefly, and I assumed it was a compromise that makers did to combat the natural physics as much as they could.

If a trombone is tuned to A=440, then fundamental frequency wound be approximately 58.3 Hz.(this is pedal Bb)

I've read that pedal tones are not actually a fundamental note on a brass instrument -- they are akin to a lip multiphonic. The fundamental would be Bb But yeah, I think it's a usually note and we can think of it that way.

Any partials that is stacked upwards have a frequency that has integer ratio with the fundamental frequency. (Let's assume that a trombone follows "perfect" harmonic series.)

It's not a perfect harmonic series. Read what Maximilien says above.

But if Aidan is right that many trombones have in fact "not-that-low" 7th partial, there must be some design element that is forcing the intonation of the partial up to that point. So that with the "forced up 7th partial" slide trombone, some can use 12tet Ab in first position, with pushed tuning slides and stick-out first position for other notes. That was the point that I wanted to say.

You were talking about the opening of possibilities in 7-limit JI, though. The OP here, Dana says you can play Ab in first in the first post. I don't think anyone here disagrees. Other than that one adjudicator.

Assume that someone is playing valve trombone, or trumpet, and, you don't have tuning option for these septimal intervals, except the 7th partial notes, with a very limited note choices.

Ahhhhh, okay, yeah I got you now. For valved instruments, maybe it would be useful if you wanted to play something 30c flat, and in the upper register, and only without any valves depressed. The problem though is that you already can pull valve slides on valved instruments, so it's better for the wonky partials on those instruments to be built deliberately sharp if possible, not flat. It's far more important on valved instruments that the partials line up closely, and having a 30 cent flat partial makes it pretty useless.

[baileyman]

My recollection from somewhere is that the history of bell tapers has been with a view toward lining up partials so positions are pretty close, especially important for valves. I would imagine there is a bell taper out there that would make a perfectly flat Ab, and it probably barks pretty good, too.

[Doldom]

But your idea that the trombone partials should match the natural harmonic series is plain wrong. Two basic reasons for that.

1) the trombone is a cylindrical pipe open at one end, and as such theoretically should only resonate on the odd harmonics, and therefore overblow at the 12th. The reason our partials appear to be like a natural harmonic series is that the bell and the mouthpiece combine in squishing the partials together, and overall raising them, approximating a normal harmonic series with all harmonics present. That we can access a harmonic series has nothing natural, it is entirely artificial and the result of the instrument's design and not direct natural properties. There would be nothing inherently more natural in a trombone that has the A 30 cents flat than one that has it playable in 1, because in reality that note is not the 7th harmonic of the pipe you're playing, it's the 15th that's been squished down by about a tritone to sound like the 7th.

2) even if this wasn't the case, and the trombone naturally produced a harmonic series, it still would not match it precisely, because the theoretical model is just that, a theoretical model. It assumes a perfect system, and in this case a tube with an infinitely small diameter. No instrument is a perfect system, all instruments have some degree of inharmonicity, because of the constraints of actually building them as physical objects in the real world.

This answer is what I wanted. Thank you for correcting me. I also have learned at physics class that an "open at one-end pipe" should resonate only on odd multipliers of fundamental frequency, but apparently the brass instrument resonates at all odd and even multipliers, so that I always felt strange about it. Apparently, physics of brass instrument is far more complex than simple "open" or "closed" tube.

I've read that pedal tones are not actually a fundamental note on a brass instrument -- they are akin to a lip multiphonic. The fundamental would be Bb But yeah, I think it's a usually note and we can think of it that way.

Yeah.. apparently, I was wrong about that. I'll study about physics of brass instruments some more and come back.

[LeTromboniste]

I've read that pedal tones are not actually a fundamental note on a brass instrument -- they are akin to a lip multiphonic. The fundamental would be Bb But yeah, I think it's a usually note and we can think of it that way.

Yeah.. apparently, I was wrong about that. I'll study about physics of brass instruments some more and come back.

The true fundamental is lower than pedal Bb, and doesn't slot.

Basically, compared to a straight pipe of the same length, the mouthpiece and bell of our instrument shifts all the harmonics up, but by different amounts so the low harmonics get shifted up further than the high ones. As you go higher and higher, the effective acoustical length of the instrument comes gradually closer and closer to the actual physical length. On lower notes, the acoustical length is significantly shorter than the actual length. In other words the shorter waves of the higher harmonics "see" a longer tube as they follow the wall of the bell, whereas the longer waves of low harmonics see a shorter tube. However, because of the huge distance between the fundamental and the 2nd harmonic (which on the straight pipe is a 12th away) the fundamental is not shifted anywhere near enough for it to land an 8ve below the 2nd harmonic even after that "squishing". It ends up somewhere around 8vb .

The pedal note we get at Bb1 (8vb ) is not a resonance of the instrument, but all of the overtones of that pitch are, and form standing waves, which is enough to force your lips to sustain a stable buzz at that non-resonance pitch. There's then at least one, maybe two effects happening that make the Bb1 heard. First the maybe: the multiphonic effect, where two or more tones sounded in the same resonator generate further tones (also physical soundwaves, and observable, but weaker) corresponding to the sum and difference of the two original tones' frequencies. I'm not sure that it has been demonstrated that this truly occurs when we play pedal tones. Second, what for sure does happens: the psychoacoustic effects of resultant tones and of the "missing fundamental". Resultant tones are like multiphonics in that they also are the sum and difference of two tones, but they are perceived tones (i.e. not observable and not actually a physical soundwave). Because harmonics are integer multiples of the fundamental, any two adjacent tones of a harmonic series will have a difference tone equal to the fundamental of that series (i.e. 3 minus 2 equals 1, 4 minus 3 also equals 1, etc). When you have enough tones that align into a portion of a harmonic series, you get several pairs of adjacent tones that all generate a difference tone at the fundamental, to the point where it can be perceived very strongly, eventually even stronger than any of the actual real sounds, thus the "missing fundamental". This is a sound your brain perceives/reconstructs, not an actual soundwave that hits your eardrum. It's the same effect they use to make 64' stops on organs: usually you don't have an actual 64' C pipe, but two pipes of 32' (C) and 24' (G) that sound together and when voiced and tuned just right, make you perceive a very loud resultant 64' C.

So when you buzz Bb1, your instrument resonates at Bb2, F3, Bb3, D4, F4, etc., and because F3 minus Bb2, Bb3 minus F3, D4 minus Bb3, and so on, all equal Bb1, you get a very strong difference tone at Bb1. Play it fortissimo and everyone will hear it loud and solid. But if you looked at a spectrogram of your sound, you'd see the strongest frequencies around 3 to 5 octaves above the fundamental, which is very atypical, and you'd see almost no actual Bb1 at all, merely the result of your buzz itself being heard, and eventually maybe of the difference tone in the multiphonic (if that's even happening at all).

Note that this is not the case in conical brass instruments, because conical pipes do produce a full harmonic series naturally. Tubas and euphoniums do not have "pedal notes" in the same sense as we do, theirs are simply the fundamental. That is why Bb1 on a euphonium feels and sound very different than Bb1 on a trombone.