Double Bass #9 or b10?

[damonsmith]

I still don't get why you keep mentioning the #4 and what point you intend to make about it: for G7 chord, the #4 (or#11) would be C#, which is not the note we were discussing here.

Concerning the coexistence of the major and minor 3rds, yes this is precisely what is happening. We have both a minor 3rd (Bb) which has a melodic role and a major 3rd (B) which gas an harmonic role (it is needed to give the G7 its dominant function). This happens all the time in minor tunes when (like in the Blue Bossa example I gave above) the melody sticks to the natural minor scale (C natural minor), even on the dominant chord (G7). The use of the natural minor scale is very frequent in a descending melodic line.

The coexistence 2 different 3rds is possible because they are voiced in different octaves (in order to avoid dissonant b2 and harmonic ambiguity) and so naturally the minor 3rd appears as a melodic b10 above the the harmonic 3.

I don't think this is something that should bother us, as it is just a musical fact (and it sounds good).

The 11 in the first post was a mistake. I am just stating the reason they don't write it as a b10 ever and you always see a #9. I also understand what you are saying, and obviously it is about adding a "blue note" but, chord notation isn't going to work that way. I think you are also sticking on a root voicing when the reality is pianists and guitarists are going to revoice chords at will - therefore your b10/#9 becomes a #4 if they decide it does in the moment.

 

[John Goldsby]

Here is what Hein van de Geyn (bass player of Chet Baker) writes about this in his excellent and thorough "Comprehensive Bass Method for Jazz Players":

View attachment 7172446

I've encountered the b10 chord symbol written by many Dutch musicians and arrangers. When I joined the WDR Big Band in 1994, I don't think I had every seen a "b10" chord symbol before. Back then, the Dutch arranger Jerry van Rooyen was working with the band a lot and he always used b10 in the situation of C7b10 (what most people would say is a C7#9). Other Dutch arrangers like Rob Pronk and Kenny Napper (the American bassist who still lives in the Netherlands, probably age 95 or so now), also used the b10 instead of #9 in their arrangements. These are brilliant musicians, so they have their own good reasons to use the b10 symbol. In a way it's more theoretically correct—even though it seems strange to most "#9-ers"! Check out some of Napper's arrangements on his website...for the famous Dutch group The Skymasters, the Rotterdam Philharmonic, The Metropol Orkest, etc. I'm attaching two little snippets of Napper's charts from our archives ... note the use of b10 in several chord symbols. E7b10#11, A7b10#11, C7b10. It looks very odd when we're used to reading and improvising over7#9 chord symbols, but the logic follows what the great bassist and teacher Hein van de Geyn is saying in the post by @Papageno. It's just another way of notating that sound that we use all the time .

 

[damonsmith]

I was not arguing what was more harmonically correct, the 10b clearly is. I was just clarifying the logic used in the #9 notation: If both notes are in play, best to give them separate names if possible.
Chord symbols are about speed & efficiency It is also reasonable to have the #9 in the chord symbol the other enharmonic note in the melody - especially in the case of Bb since Bb is so much more common than A# in notation. Charts are not scores and charts are about getting the job done, not about neatly fitting into the rules of music theory.
In any case, there are strong arguments for both & neither is strong enough to force change in existing charts & a good musician should not be vexed by either.

 

[damonsmith]

Did anyone already say that reason it is called an 11 that the 4 is not already in the chord? If possible, it is best to add an interval name that is not there. Calling it a 10b is not ideal, because the voicings are improvised and the 3rd that is already there can end up in the same octave as the added #4.

Sorry, I meant #2 and that the reason is the 2 is not already in the chord.

 

[DoubleMIDI]

As I said before, chord naming is not theoretically correct but helps for getting a good voicing (mostly with #5 where it is really a b13, because the pure fifth is in the scss as less).

It does not make sense to discuss the #9 vs. b10 if chord notation is still not theoretically correct in other places.
The problem is that nobody tells you that chord notation is not theoretically correct.

So this discussion should be split into “Should chord notation be modified to be theoretically correct and which consequences might that have for playing?” and “In which scale should we use #2/#9, b3/b10, b5, #5, b6/b13 to be theoretically correct and how do we handle 8-note scales?”.

We need to separate chord symbols as hints for voicings and theoretically correct notation (of 7-note scales).

 

[Tom Lane]

I've learned a lot of things on TB, most of it related to music, but also some on-line social behaviors. One rule I made for myself some time ago is to not repeat myself in a theoretical discussion and that's because I find that if the conversation has come back around to where I feel the need to repeat myself, it means that the conversation is no longer a conversation. IMO of course, but you do you.

 

[DoubleMIDI]

If one thinks that a #5 means that there is no pure fifth and therefor not be playing the pure fifth during improvisation, that would lead to a strange choice of notes if the #5 is theoretically incorrect and should have been a b13.
Same for #9 vs. b10.
It is not so much for theoretical correctness per se, but if deriving from a sloppy notation leads to a wrong choice of notes during improvisation.

 

[longfinger]

If one thinks that a #5 means that there is no pure fifth and therefor not be playing the pure fifth during improvisation, that would lead to a strange choice of notes if the #5 is theoretically incorrect and should have been a b13.
Same for #9 vs. b10.
It is not so much for theoretical correctness per se, but if deriving from a sloppy notation leads to a wrong choice of notes during improvisation.

If I found a 7(#5) symbol , I would not play the natural 5th, but play a #5, or a b5.
If I found a 7(b13) symbol, I would play the natural 5.
Those are different chords, for different situations, and many folks recognize that.

 

[DoubleMIDI]

If I found a 7(#5) symbol , I would not play the natural 5th, but play a #5, or a b5.
If I found a 7(b13) symbol, I would play the natural 5.
Those are different chords, for different situations, and many folks recognize that.

It is not about what notes in the chord will be played, but how to derive the scale that matches the chord (well, also the chord in its context). So, it’s about deciding which notes in a ascending or descending line in improvisation over this chord should be played.
It is also important for stepwise (not broken chord) walking basslines.

Theory is not only for analysis, but also for helping choosing the right notes during playing.

The #5 is often a theoretically wrong shortcut notation for a chord that would not fit the scale which has a pure fifth and a minor sixth in it.
Some chord symbols may tell you that it is really a b6/b13, but this is often not unambiguous and one needs to think around one corner more.

The use of enharmonic notation (mainly in jazz) might be easier to read for the single note, but harder to understand which function this note has. So it can easily mislead in improvisation.

This is not a problem for players ignoring the written chord symbols in improvisation and playing by ear only. But they ignore correct notation in theory as they do not distinguish between the enharmonics and their function.

 

[longfinger]

It is not about what notes in the chord will be played, but how to derive the scale that matches the chord (well, also the chord in its context). So, it's about deciding which notes in a ascending or descending line in improvisation over this chord should be played.
It is also important for stepwise (not broken chord) walking basslines.

Theory is not only for analysis, but also for helping choosing the right notes during playing.

The #5 is often a theoretically wrong shortcut notation for a chord that would not fit the scale which has a pure fifth and a minor sixth in it.
Some chord symbols may tell you that it is really a b6/b13, but this is often not unambiguous and one needs to think around one corner more.

The use of enharmonic notation (mainly in jazz) might be easier to read for the single note, but harder to understand which function this note has. So it can easily mislead in improvisation.

This is not a problem for players ignoring the written chord symbols in improvisation and playing by ear only. But they ignore correct notation in theory as they do not distinguish between the enharmonics and their function.

Yes, I know that. That's why the chord symbol will influence what palette of notes I would choose from.

The b13 chord mislabeled as #5 seems very 1970s to me. I don't think that happens much anymore. At least not like before. People make better chord symbols now based on the entire 7 note palettes (scales when stacked in seconds, arpeggios/chords when stacked in thirds, but same notes.) and better naming conventions. IME/IMO.

 

[DoubleMIDI]

…

The b13 chord mislabeled as #5 seems very 1970s to me. I don't think that happens much anymore. At least not like before. People make better chord symbols now based on the entire 7 note palettes (scales when stacked in seconds, arpeggios/chords when stacked in thirds, but same notes.) and better naming conventions. IME/IMO.

Not by my experience reading modern big band charts.
There are often even more simple errors like notating a Gb instead of a F# in a D major chord type. Not pleasant to read and makes it harder to derive the harmony from the notated Bassline.

The reason (beyond the arrangers or arrangements are still a bit older) might be that when a b13 is notated, it usually means with 9 and 11, which typically results in a different chord played than what is played for a #5.
Try that with automatic chords from chord symbols in iRealb, Band-in-a-box, MuseScore or similar.
It more clearly shows what notes to use for the chord, but on the expense of not being theoretically correct.
I doubt that this will change for the ease of finding a good voicing.

What is missing is a clear hint during education and in books with examples that deriving a scale assuming the modifiers are theoretically correct can be heavily misleading. Specially for those who know classical harmony well.

 

[MuseChaser]

I haven't read every post in this thread, but I did read a lot of them. If the following has already been said by another poster (or more), my apologies.

One of the many difficulties with internet discussions is that opinions are quite often stated as facts, rather than opinions, and things then become heated. Having said that, I recognize that what I am about to write is my opinion, but it makes perfect sense to me. I've taught jazz theory and jazz piano at several universities, and have worked with many of the world's best jazz players, so my opinion is not without at least some background. Still... there will always be room for argument.

My father, a top-flight trombonist and arranger who wrote for the Glen Miller band (among others) back in the late 50s and early 60s, calls the chord in question a "b10" chord, and notates it that way in all of his big band charts (he's written hundreds). In his book, that nomenclature can be found in other noted arrangers' work from that period, also, while other arrangers chose to use "#9." He and I have had LENGTHY discussions on the subject over many decades, and my assertion that it's a #9 (I'll get to my reasoning soon, I promise) caused him enough consternation that he actually wrote a chart entitled "It's Really a Flat Ten!" in response, utilizing that chord frequently throughout.

OK... here's why it's NOT a b10, and IS a #9 (in my opinion...but if you think otherwise, you're wrong... hahahaaha...).

First commonly accepted rule to state - any chord with a number higher than 7 implies the inclusion of the seventh, and the included 7th is a b7 unless otherwise clearly notated. Alright, we got that out of the way.

Let's take C7b10 as an example. It's based upon a C dominant 7th chord, C, E, G, Bb. So far so good. What's the 10th of C? It's E. If we flat the E, there is no longer an E natural in the chord at all, but only an Eb. Now we have C, Eb, G, Bb, and that's it. That's a C minor 7th chord. The nomenclature is just wrong.

Now let's look at C7#9. Again, based upon a C dominant 7th chord, C, E, G, Bb. What's the 9th? It's a D. Raise it to D#. There is no longer a D natural in the chord, but there is still the regular major third, the E, so we still have the basic dominant 7th chord intact, with the added tension color of the raised 9th D#.

Chords with altered extensions almost always (and in my opinion, should ALWAYS) alter the odd numbered extensions only, leaving the the root, third, and fifth as either major, minor, diminished, or augmented triads. The even numbered extensions past the octave duplicate these important foundation tones, and therefore, if altered, change the base triad function. To expound a bit further, a C7#5 (better written as C+7, in my opinion, indicating the triad quality first and then the extension), is a C augmented triad with a flat 7, containing a G# and NOT a G at all, while a C7b13 would be a C dominant 7 base with an added Ab, retaining the unaltered G within the chord voicing.

 

[Tom Lane]

I haven't read every post in this thread, but I did read a lot of them. If the following has already been said by another poster (or more), my apologies.

One of the many difficulties with internet discussions is that opinions are quite often stated as facts, rather than opinions, and things then become heated. Having said that, I recognize that what I am about to write is my opinion, but it makes perfect sense to me. I've taught jazz theory and jazz piano at several universities, and have worked with many of the world's best jazz players, so my opinion is not without at least some background. Still... there will always be room for argument.

My father, a top-flight trombonist and arranger who wrote for the Glen Miller band (among others) back in the late 50s and early 60s, calls the chord in question a "b10" chord, and notates it that way in all of his big band charts (he's written hundreds). In his book, that nomenclature can be found in other noted arrangers' work from that period, also, while other arrangers chose to use "#9." He and I have had LENGTHY discussions on the subject over many decades, and my assertion that it's a #9 (I'll get to my reasoning soon, I promise) caused him enough consternation that he actually wrote a chart entitled "It's Really a Flat Ten!" in response, utilizing that chord frequently throughout.

OK... here's why it's NOT a b10, and IS a #9 (in my opinion...but if you think otherwise, you're wrong... hahahaaha...).

First commonly accepted rule to state - any chord with a number higher than 7 implies the inclusion of the seventh, and the included 7th is a b7 unless otherwise clearly notated. Alright, we got that out of the way.

Let's take C7b10 as an example. It's based upon a C dominant 7th chord, C, E, G, Bb. So far so good. What's the 10th of C? It's E. If we flat the E, there is no longer an E natural in the chord at all, but only an Eb. Now we have C, Eb, G, Bb, and that's it. That's a C minor 7th chord. The nomenclature is just wrong.

Now let's look at C7#9. Again, based upon a C dominant 7th chord, C, E, G, Bb. What's the 9th? It's a D. Raise it to D#. There is no longer a D natural in the chord, but there is still the regular major third, the E, so we still have the basic dominant 7th chord intact, with the added tension color of the raised 9th D#.

Chords with altered extensions almost always (and in my opinion, should ALWAYS) alter the odd numbered extensions only, leaving the the root, third, and fifth as either major, minor, diminished, or augmented triads. The even numbered extensions past the octave duplicate these important foundation tones, and therefore, if altered, change the base triad function. To expound a bit further, a C7#5 (better written as C+7, in my opinion, indicating the triad quality first and then the extension), is a C augmented triad with a flat 7, containing a G# and NOT a G at all, while a C7b13 would be a C dominant 7 base with an added Ab, retaining the unaltered G within the chord voicing.

I agree with most of this. Acknowledging that you're infinitely more qualified to make this assessment than I am, I think the failure in your reasoning is that a chord can't have both a major third and a minor third, or a Major 3rd and a b10. A b10 is not a b3, it's a b10, a different animal. I think your reasoning would hold if we tried to notate a chord as a C7b3. In that case, I would expect that there is no Major 3rd, but a b10 is an extension, so I would expect a C7b10 to be comprised of any of the following pitches, C E G Bb D Eb, depending on how the harmonist wanted to voice it. Granted, that D probably won't be used much, but it could if the context suited it.

But the fact that you and your Dad haven't resolved the debate indicates that we never will either.

 

[MuseChaser]

I agree with most of this. Acknowledging that you're infinitely more qualified to make this assessment than I am, I think the failure in your reasoning is that a chord can't have both a major third and a minor third, or a Major 3rd and a b10. A b10 is not a b3, it's a b10, a different animal. I think your reasoning would hold if we tried to notate a chord as a C7b3. In that case, I would expect that there is no Major 3rd, but a b10 is an extension, so I would expect a C7b10 to be comprised of any of the following pitches, C E G Bb D Eb, depending on how the harmonist wanted to voice it. Granted, that D probably won't be used much, but it could if the context suited it.

But the fact that you and your Dad haven't resolved the debate indicates that we never will either.

Thanks for replying, Tom. When one "voices" a chord, as a pianist, guitarist, vibist, organist, arranger, or any other musician deciding how to play a given chord, one very rarely plays it in a stacked root position. To use your example, "C, E, G, Bb, D, Eb" would not be played that way, nor is it typical or advisable practice to notate chords with differing accidentals on the same letter-named note. While musicians do indeed regularly fill in chords with extensions above the 7th as their ear and practices within specific genres dictate, only the b7 is implied with extensions above the octave; a b10 would not require the inclusion of a D, while a #9 WOULD require the inclusion of a D# and would also REQUIRE the omission of a D natural. A common voicing for this chord would be a C in the bass or on the bottom, an E a tenth above, then a Bb a tritone above that, then a D# (which you refer as an Eb) an augmented third (same distance as a perfect fourth) above that. That voicing gives a full rich sound, maintaining the intended tonality and function of the chord without being too muddy or crunchy.

Just to be clear, my responses have been addressing chord function, structure, and notation. There a zillion ways to navigate chords when constructing melodies, and a D natural could certainly be used as an approaching, passing, or neighboring tone while improvising a melody OVER that chord, but one would rarely choose to sit on a D natural for any length of time over a C7#9, nor would one notate that chord using an Eb within the chord.

Edit: One more thing I meant to add, or at least be more clear about....

There are seven "cardinal" notes, or naturals...ABCDEFG. Chords are typically constructed using only one version or alteration of those notes. When you described chords as being able to have a major 3rd AND a b10, that isn't really correct. It seems to me that you are conflating intervals (distances between notes) with scale degrees. The 3rd and the 10th in the key of C major are both E, period. Which octave they are in matters not. However, if we're speaking about intervals rather than scale degrees, then yes, a major third above C, two whole steps, would be an E, while a minor or flat tenth above C, would be an Eb, a distance of an octave plus a whole step and a half step. That distance could also be described as an augmented (or sharped) ninth, in which case the note would have to be called a D#. Intervals and chord degrees are different animals because chords can be voiced so many different ways (the 7th is frequently placed below the third, for instance), while intervals are just absolute distances between notes regardless of key or tonality.

Occasionally you'll see someone write something like C+7b9#9#11b13, in which case, yeah, there's two versions of D (Db and D#) but at that point, well ...you may as well just smash your forearm on the piano anywhere you want to ..hahahaha.

 

[Tom Lane]

Thanks for replying, Tom. When one "voices" a chord, as a pianist, guitarist, vibist, organist, arranger, or any other musician deciding how to play a given chord, one very rarely plays it in a stacked root position. To use your example, "C, E, G, Bb, D, Eb" would not be played that way, nor is it typical or advisable practice to notate chords with differing accidentals on the same letter-named note. While musicians do indeed regularly fill in chords with extensions above the 7th as their ear and practices within specific genres dictate, only the b7 is implied with extensions above the octave; a b10 would not require the inclusion of a D, while a #9 WOULD require the inclusion of a D# and would also REQUIRE the omission of a D natural. A common voicing for this chord would be a C in the bass or on the bottom, an E a tenth above, then a Bb a tritone above that, then a D# (which you refer as an Eb) an augmented third (same distance as a perfect fourth) above that. That voicing gives a full rich sound, maintaining the intended tonality and function of the chord without being too muddy or crunchy.

Just to be clear, my responses have been addressing chord function, structure, and notation. There a zillion ways to navigate chords when constructing melodies, and a D natural could certainly be used as an approaching, passing, or neighboring tone while improvising a melody OVER that chord, but one would rarely choose to sit on a D natural for any length of time over a C7#9, nor would one notate that chord using an Eb within the chord.

Edit: One more thing I meant to add, or at least be more clear about....

There are seven "cardinal" notes, or naturals...ABCDEFG. Chords are typically constructed using only one version or alteration of those notes. When you described chords as being able to have a major 3rd AND a b10, that isn't really correct. It seems to me that you are conflating intervals (distances between notes) with scale degrees. The 3rd and the 10th in the key of C major are both E, period. Which octave they are in matters not. However, if we're speaking about intervals rather than scale degrees, then yes, a major third above C, two whole steps, would be an E, while a minor or flat tenth above C, would be an Eb, a distance of an octave plus a whole step and a half step. That distance could also be described as an augmented (or sharped) ninth, in which case the note would have to be called a D#. Intervals and chord degrees are different animals because chords can be voiced so many different ways (the 7th is frequently placed below the third, for instance), while intervals are just absolute distances between notes regardless of key or tonality.

Occasionally you'll see someone write something like C+7b9#9#11b13, in which case, yeah, there's two versions of D (Db and D#) but at that point, well ...you may as well just smash your forearm on the piano anywhere you want to ..hahahaha.

Again, we agree on a lot of this. Particularly a chord specified to have both a b9 and a #9 being a "whack the piano" chord!

When I spelled out the C7b10 chord as C E G Bb D Eb I wasn't specifying its voicing. Anything is possible of course, depending on the situation and the context, but I'd probably start a rootless voiced C7b10 as E A Bb Eb, adding the 13th and having a Major 7th interval between the E and Eb.

Lastly, I think the convention is when we're specifying extensions, pitches above the octave, 9, 11, 13th, etc, that we're usually expecting them to be "color" pitches and expecting them to be among the higher pitched notes of the chord, so in mind, there's no confusion by specifying a C7b10 because I'll assume that the E is going to be voiced below the Eb. Maybe that's a lot of unwritten assumptions, but it seems consistently logical to me.

 

[MuseChaser]

....so in mind, there's no confusion by specifying a C7b10 because I'll assume that the E is going to be voiced below the Eb. Maybe that's a lot of unwritten assumptions, but it seems consistently logical to me.

Thanks again. I understand what you're saying, and in practice whatever is most clear and consistently logical to you is fine. As a pianist who has to, on many occasions, read some really crunchy voicings, it's really nasty to see an E and an Eb in the same chord, especially since standard notation practice is for an altered note to remain altered within a given measure until corrected by a natural sign. This confusion can be further compounded when playing manuscripts written in the Baroque era and back, when accidentals not only carried through the bar, but also tended to carry through different octaves.

To me, it is eminently more logical to write a D#, since a D is no longer part of the chord anywhere, and consider the chord to be a #9 for that reason in addition to the reasons already mentioned. Melodically, of course, D# and Eb are enharmonics and the same note (on a fixed pitch instrument anyway), but harmonically/chordally, I don't find them logically interchangeable.

 

[Tom Lane]

Thanks again. I understand what you're saying, and in practice whatever is most clear and consistently logical to you is fine. As a pianist who has to, on many occasions, read some really crunchy voicings, it's really nasty to see an E and an Eb in the same chord, especially since standard notation practice is for an altered note to remain altered within a given measure until corrected by a natural sign. This confusion can be further compounded when playing manuscripts written in the Baroque era and back, when accidentals not only carried through the bar, but also tended to carry through different octaves.

To me, it is eminently more logical to write a D#, since a D is no longer part of the chord anywhere, and consider the chord to be a #9 for that reason in addition to the reasons already mentioned. Melodically, of course, D# and Eb are enharmonics and the same note (on a fixed pitch instrument anyway), but harmonically/chordally, I don't find them logically interchangeable.

Ah, so I think that's a good point. I think there's a big difference between specifying a chord symbol of C7b10 and notating a chord in a score with both an E and Eb, if I read you correctly. I do think it would be confusing on a score although I suppose you could put a Natural sign in front of the Major 3rd and a flat symbol on the Minor 3rd. I suppose, again, it would depend on the context. Assuming we're talking about a piano score, then the two E's would be on different staves and then I think it'd depend on the notes that follow. Is it more difficult to read a D# followed by a Natural D or an Eb with an E Natural on the lower staff? I think probably the Eb is more confusing in that case. I don't think I've ever seen a b10 notated before John Goldsby's examples. I think the convention is to use the #9 and think of it as an altered chord, which unless the scorer is being very particular, means that the voicing can contain any or all of the altered extensions. Personally, I don't take any leadsheet literally because it's jazz and I want to make the tune mine. It'd be different if I were being paid to record someone's composition.

 

[DoubleMIDI]

Write down the scale for a given chord. A b9#9 is typically an 8-note scale, so one basic pitch name needs to be doubled. In some cases hard to decide which one and easier in others.
In some (i.e. altered = mMin VII) the function of the notes in the chord might dictate the use of an enharmonic in a chord, but probably not in a melodic line.

A more logical use of odd vs. even numbers does not necessarily lead to a music theoretically correct use.
If the (typical) melodical use in a line is either major or minor third, then a major chord with a b10 is theoretically correct.

A maj7#5 can be correct like for mMin III, but incorrect for hMaj I where it is a b13.

 

[MuseChaser]

Write down the scale for a given chord.

In my experience (and opinion), that is not possible, as there is no "the" scale for any given chord. Scales are made up of chord tones and passing tones, and the manipulation and altering of the passing tones can be the heart of creative melodic improvisation. As such, there can be a myriad of effective "scales" to choose from when playing over a specific chord. It's two different things

A b9#9 is typically an 8-note scale,

I apologize for the repetition, but, for example, a C7b9#9 is not any kind of scale; it's a chord.

so one basic pitch name needs to be doubled. In some cases hard to decide which one and easier in others.
In some (i.e. altered = mMin VII) the function of the notes in the chord might dictate the use of an enharmonic in a chord, but probably not in a melodic line.

If I'm understanding you correctly, I view it the opposite way. Chord structure and nomenclature clearly dictates what terms should be used, while single line melodic notation often uses enharmonic notation for certain chord tones used within a melody in order to minimize accidentals and facilitate reading.

A more logical use of odd vs. even numbers does not necessarily lead to a music theoretically correct use.

Again, to my mind it definitely does. Music theory evolved as a logical way to describe what we do and gives us standard ways to communicate advanced concepts.

If the (typical) melodical use in a line is either major or minor third, then a major chord with a b10 is theoretically correct.

Perhaps it's my life as a jazz pianist informing my thoughts (ok...more than perhaps), but if a melody uses both versions of the third note of the scale per your description, one of a few possibilities exist. Either it's a minor chord of some kind and the major third note is used as a fleeting passing tone either descending to the minor third or rising to the fourth, or as part of a bitonal arpeggiation that will, hopefully, lead to the minor tonality of the chord in question, OR it's a major chord and the minor third is used in the same fashion, OR it's a dominant 7 chord and the minor third is used not as a "minor third" but rather as the #9 tension note. In none of those cases does calling it a b10 make as much sense to me; it's either the minor third if used in a minor chord or as a passing tone, or a sharp ninth if it's part of the chord. As I said in an earlier post, there seems to be confusion between chord nomenclature, scalar nomenclature, and intervals.

A maj7#5 can be correct like for mMin III, but incorrect for hMaj I where it is a b13.

I confess I don't understand your shorthand here completely. A maj7#5 (which I previously suggested is better named a +maj7 where the "+" indicates augmented, as it address the structure of the root triad first prior to the alterations) "can be correct like for a mMin III"... do you mean for a III chord? If so, do you mean in a major or minor key? What do you mean by mMin...typically, a lower case m means minor, so mM could mean "minor major," but I've never seen mMin before. Likewise, "hMaj I" also confuses me...a "I" chord with a ...half major?

This is why I advocate, admittedly strongly, for a consistent approach to chord nomenclature. A "maj7#5" chord will ONLY have the #5 in it...no other versions of the fifth...and a major 7th, while a b13 chord will have a flatted thirteenth (an enharmonic spelling of the #5) but will also retain the unaltered fifth and a flat 7th. They are not the same chord at all.

 

[longfinger]

My father, a top-flight trombonist and arranger who wrote for the Glen Miller band (among others) back in the late 50s and early 60s, calls the chord in question a "b10" chord, and notates it that way in all of his big band charts (he's written hundreds). In his book, that nomenclature can be found in other noted arrangers' work from that period, also, while other arrangers chose to use "#9." He and I have had LENGTHY discussions on the subject over many decades, and my assertion that it's a #9 (I'll get to my reasoning soon, I promise) caused him enough consternation that he actually wrote a chart entitled "It's Really a Flat Ten!" in response, utilizing that chord frequently throughout.

Can you summarize your Dad's reasoning on the b10chord name?