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How do you learn by ear?

Would you care to provide a real world example where a major 6 chord functions as a V? That would really help to understand your position.

Your question drove me through the Realbook, and sweating heavily, phew..:)

I started looking up the obvious examples: There will never be another you, I can't give you anything but love, Darn that dream, Paper Doll...
- all of them with melodies ending from maj. 3rd (the 6th to V) to key - only to find out that all of those composers wrote a dom7th chord under that note like if their noses were bleeding... a good lesson in humility. I really would like to know why they did that, writing 6th against 7th just like that. Probably Ed Fuqua knows this.

Far more common, (especially around the 1940's) - as Ed explained - the 6th is used to color certain chords. The 6th is not the melody note, and certainly not the intended bass note (like b5 or b9 sometimes are), it's just there to add some varnish. In many cases, you''ll find this feature in song endings -they are all over the RealBook. The harmonic function there is - I -, of course.

Nice case of 6th-chord as subdominant is the famous plagal ending of My Way (F6 to C), where the 6th is the melody note.

And now for the dominant 6th... (drum roll, please). They were not as common as I thought they would be. But two clearcut examples from the RealBook where a 6th chord is dominant are Hot Toddy and Wives and Lovers.

Anyway, all of this only underlines the importance of being aware of harmonic functions, wether we play them or write them.
 
In response to the OP:

I use MacBook only, so I have no view as to PC only programs. But I have downloaded and worked with the demos of three programs for my Mac. They strike me this way.

Audiolobe - Changes tempo and pitch on the fly right from the main interface with either keys or mouse. Lets you select pitch in semitones. Lets you loop and save loops. Lets you record, save, and playback your own instrument over a play-along over the air using your built-in (or added) speakers and mic. $20.

Transcribe! - Changes tempo and pitch on the fly, using a series of drop-down menus. Lets you select pitch in semitones and even cents. Lets you loop and save loops. Has graphic wave-form display to visually find certain spots in the recording precisely. No ability to record your own instrument over a play-along, that I could find. $50.

Audacity - Changes tempo and pitch by making copies of a tune, or part thereof, in a new file each time--then you play back the new file. Lets you loop and save loops. You can record your own instrument over a play-along because it has tons of music file editing features--including recording, multi-track mixing, and play back features that I cannot evaluate because I'm not into editing. Free, I think.

For me, I was interested in learning from play-alongs and other CDs and recording myself over them for evaluation purposes--and also manually transcribing during audio playback. Audiolobe does this all, and the most easily. I don't see the need for viewing a wave-form diagram while I'm doing this. The sound-on-sound recordings are certainly not commercial CD quality, being over-the-air recordings out of your Mac's speakers, but all I need is the ability to evaluate my rhythm, intonation, and articulation while using play-alongs, which Audiolobe lets me do. The developer states that he intends to continue adding improvements, such as an equalizer instead of tone controls and direct access from iTunes library. But for me, it's already almost ideal.

Using any playback program, you have to swing over your balance control when you want to remove bass from most play-alongs. This puts the remaining sound in one ear only, which I find weak and unnatural. To put the non-bass sound in both ears, I made a 6" adaptor from parts at Radio Shack. This makes playing with play-alongs much more natural sounding and more enjoyable. I made a second adaptor that does the opposite, putting the bass in both ears, for transcription purposes. These two adaptors cost me under $10 to make. So, with Audiolobe and these two adaptors, I think my MacBook is pretty well set up for practice with play-alongs, performance CDs, mp3s, mp4s, etc., and for manually transcribing off of them.
 
Easy, learn the number system. With that you get the intervals and when you listen to music you will learn it, or figure it out, easier. All the dominate 6th and 13th crap...that comes with experience and mainly with regular guitars. A lot of jazz bassists use that and maybe really good bassists, which I am sure he MUST be or he wouldn't talk about it. Start with some blues for the number system to get the intervals down and then work on more difficult songs.
 
I've been playing bass for a while now and I'm seeing improvements but I'm still really really struggling to transcribe things by ear. Has anybody got any good methods of learning by ear?

By ear means by ear

I started at 5 years old. i did not know from intervals

Just match what you hear to your bass

Amazing Slow Downer is a great tool to slow stuff down

Also sing what you hear- not as easy as u think

Play by ear means no knowledge just instinct
of course knowledge MAY help
but developing ear is terrific

copy melodies and variations of melodies riffs licks too
 
Listen to the bass part until you can sing it. Then play it.

Singing what you hear, as in above is good too

I know a player who transcribed in the following way

Instead of writing it down after he listened to a phrase
he skipped the writing down, and jumped right to the playing

He did this with all kinds of jazz records, not just on his main ax, but on other instruments as well
What an ear he has!!!