Grace

Full Band

The Birkat Hamazon, the grace after meals, has a very fun traditional melody (which apparently dates to 80 years ago or so), so I decided to set it for band. On Shabbat and festivals, the Birkat Hamazon is preceded by Psalm 126, labeled (like many others in that section of the Tanach) "Shir Hamaalot", or "Song of Ascents", where the meaning of "ascents", according to my JPS Jewish Study Bible, is unclear and possibly refers to steps of the temple or something similar. Here, then, I have set this Song of Ascents for wind orchestra, with an attempt to emulate, to some extent, Percy Grainger. The Birkat proper will follow.

Listen to Grace - I - Song of Ascents (right-click to download)

Irish Tune

I have before me the score to Percy Grainger's vocal setting of the Irish Tune from County Derry, set in 1902, and published in 1912, the same year as a songwriter first published some words he had written earlier with the same tune, the words being named "Danny Boy". Apparently, the song is not so Irish:

http://www.standingstones.com/dannyboy.html

That's a very interesting explanation of the history of this song known by Americans everywhere as Danny Boy and connected to Ireland, and it attempts to explain why it's so completely uncharacteristic of Irish music at the time it was collected. But say what you will about Percy Grainger and his personal beliefs and habits, this is a frickin' masterful setting, and I really want to learn how to write like this. Here's one version played by a string orchestra. It's exactly the same as the choral version I'm looking at, except it's played by strings instead of voices (the voices actually do some cool stuff with humming and vowels, but that's not the relevant point), and the first half of the second time through the melody is up an octave.

http://www.youtube.com/watch?v=x7w9vVGnxvA

Anyway, Grainger is awesome -- he's very particular about writing directions in English. No "cresc." or "dim." Instead, you find "louden lots" and "slow off lots" and "much to the fore" and "accompanyingly". I just thought that was exceedingly cute. The point of this is that I actually want to learn to write like he does and compose a similar setting for other music, namely a particular melody for Shir Hamaalot. The tune's apparently by a P. Minkowsky. I can't tell when this recording is from, but the cantor in it died in 1933, so it's got that beautiful grainy sound you get from old music.

http://www.chazzanut.com/rosenblatt/rosenblatt-notes.html

The eventual goal here is to compose a wind orchestra setting for the entire Birkat haMazon, the Jewish grace after meals, and while the Shir Hamaalot is not exactly part of the Birkat itself, it's sung before it, as part of the ritual, on Shabbat. The real challenge will be to make the chanting in the body of the Birkat playable by an ensemble and not boring. The Birkat haMazon is a rather long series of blessings, about six to seven minutes in total, mostly split between chanting and very upbeat major melodies with motifs that repeat throughout. Apparently this is generally due to Mordecai Kaplan in the 1920's (http://jewsbychoice.org/2007/10/25/jewish-ritual-on-the-rise-in-america/), though there's one section in there that's often sung to a tune very different from the rest of it -- it's got a minor mode, unlike the rest of it, and sequences, which suggests a more modern Israeli style. You can see the Pesach version in the Harmoniot shel Pesach:

http://web.mit.edu/braunst/www/Harmoniot.pdf

Anyway, I'll post when it's completed, if ever. The Shir Hamaalot will be first, and separate; to make the analogy even further, and this isn't exactly out of emulation but because it's just working this way, it will be like Grainger's publication for band, with Irish Tune from County Derry and Shepherd's Hey (a much faster and upbeat tune) on the same sheet of paper, like a B-side, if you will. I also want to learn how to write like he writes his fast music, but that's for later. (:

Oro y Tomates

2 trumpets (in C), horn, trombone

My brother asked me to write a brass quartet, STAT, and to make it sound Spanish. So I did it. I tried to also make it sound a little Jewish, so you can actually pick out some Jewish notes in there (if you think you've heard that snippet before in synagogue, well, you have). Oh, and the first measure is (seriously) based on Jungle Hijinx! from Donkey Kong Country, or whatever the actual name of the song is. The inspiration really went no further than the rhythm of the first measure, but it's what it is. But there's some neat stuff in there; it's a fun piece.

Listen to Oro y Tomates (right-click to download)

Suite of the Undead

2 trumpets, 2 horns, trombone, euphonium, tuba

The 2008 entry to the BCMW contest. The idea of a march of the undead had been floating in my head for a LONG time, and I had a little tune for it, so I figured that this time, this time, I'd actually write it, and it ended up as the second movement in the suite. The requirements were somewhat different -- many movements, 13-15 minutes total, rather than three movements of around 5 minutes each -- and I, uh, well, it's too long by about a minute and a half, but I imagine it could be sped up. Oh, the creatures mentioned in the piece are Exile/Avernum-style undead -- a zombie is supposed to be a magically reanimated corpse that can be killed in a few hits (a few WEAK hits) rather than a horrible-virus-infected supermutant that zombifies on contact, though I suppose a lich may be powerful enough to do that. Or a zombie dragon (GAH, FF5!). Oh, cool note: LOTS OF SPECIAL EFFECTS! You can't really hear all of them faithfully, but the horns will do some, uh, surprising things. (: And there's some rather creative orchestration at times, with trombone down in the pedal range, euphonium an octave higher in the low range, and tuba an octave higher than the euphonium, playing fairly high. High tuba is generally underexplored, I think. At least by me.

Listen to Suite of the Undead - I - Awakening: The Lich (right-click to download)
Listen to Suite of the Undead - II - March of the Zombies (right-click to download)
Listen to Suite of the Undead - III - The Vampire's Lullaby (right-click to download)
Listen to Suite of the Undead - IV - The Werewolves' Hunt (right-click to download)
Listen to Suite of the Undead - V - Ghostly Lament (right-click to download)
Listen to Suite of the Undead - VI - Finale: The Lich (right-click to download)

The Three-Body Problem

Whenever I read harmony books I get ticked off at the sophomoric explanations of harmonic phenomena that are ever present. I should correct that and use the past tense, actually, because the harmony books in which I find these tend to be older, apparently before the concept of observation was developed. Hindemith, in particular, talks about combination tones and their overtones to discuss consonance, and I find that rather silly. He also says that intervals have roots.

What is the root of a given interval? For the major third, for instance, it's the bottom member; for the minor sixth, its inversion, the top member. How does he know? See, I disagree with him, because one would have to consider the interval in a vacuum to identify a root, and an interval is never in a vacuum! I hold that context is critical, and that the tonal center forms a third note around which the two notes of the interval gravitate. When trying to figure out the "meaning" of an interval, the (local) key is an inseparable part of the problem. Hence we have a three-body problem, which complicates the simplicity of a two-note interval with necessary ambiguity.

My favorite example is the major sixth, because either note can be the "root". What's worse, if the major sixth is G E and the key of C is well-understood, the root is the C, a note not even in the interval! If an E minor harmony is implied, E is the root; if a dominant function in the key of C is implied, G is the root. If the interval is present by itself, without any context -- or, rather, with itself as its context -- a trick of the ear can change the root, like the spinning dancer or the cube that looks like it's either coming out of the page or into the page. The beautiful simplicity of the analysis of only two tones is, sadly, not to be.

I hope that this helps dispel the notion that the overtone series has much to do with harmony beyond providing the fifth. That notion needs dispelling, and any little bit counts.

Interval of the Moment

Diminished octave. In particular, in Villa-Lobos's Suite Popular Brasileira, V - Chorinho, where there's a held low E in the bass, struck D G# B in the middle, and struck G natural in the melody. It's obviously a dominant 7th chord to A minor, even though it doesn't actually resolve that way; the G natural goes down to F then E. It's the clash of the two natures of "traditional" melodic minor that sounds so great.

Another great interval is the diminished third, especially between the raised 7th and lowered 2nd, as used melodically in Tarrega's Recuerdos de Alhambra (which, unlike the Villa-Lobos, I have not yet attempted to play; the right hand figuration is HARD). One phrase ends on the G#, the 3rd of the dominant 7th of A minor, and the next one begins on Bb, the b9th of the secondary dominant to D minor. The melody: C B A B A G#; Bb A G A G F... The first few times I heard it, I couldn't identify the interval. It's just so remote -- a diminished 3rd -- and it was THAT interval that led me to realize that a diminished 3rd is NOT the same as a major 2nd. Ah, context.

The Value of Planning

Every year I participate in a great competition that requires a composition for brass ensemble of varying size (this year, a septet) of around 15 minutes. It's a great chance to write something with a deadline, since it's due February 1st, and I do something different every year. I've been working on this year's entry lately, and I realized something everyone already knows: planning is GOOD. Editing is GOOD. Showering is GOOD.

The problem is that it takes a lot longer to write something than to sing something or think about something, so sections end up being too short. I get bored writing even short segments because it takes so much longer than the segments themselves, so my writing ends up all over the place because my ideas change much more quickly than the music. I'm finding, then, that it's a good idea to think about how things will develop in the shower, try to remember them, and write them in. Things sound much better in my head than they do once I've written them, but also, once I've written them, I can't really think of them any other way, so this is hard to do.

One thing that I used to not understand until very recently was how composers could write music that doesn't sound great throughout, with some boring moments. I think I understand now that it's for pacing reasons, because otherwise the piece isn't balanced. There needs to be time with nothing important happening so that important things are more important. Filler material, if you will, that serves to continue the piece until what needs to happen can happen. It's also a great time to introduce new motifs, or to quote old ones. There's an art to writing "boring" music as well.

Everyone already knows this, but that's what I figured out today. (: I'll hold off on details of the piece until I hear back from the competition to maintain the anonymity of my piece.

In Which I Rant About The Overtone Series

GAH. I'm reading through Hindemith's "The Craft of Musical Composition", and like every other book written about music, no introduction is complete without a discussion of the overtone series. And somehow, maybe because they're musicians rather than physicists, it's ALWAYS unsatisfactory. I've NEVER seen the overtone series explained correctly except in the Griffiths Intro to Quantum Mechanics book. Yeah, QM, not music theory. It's ridiculous. The overtone series isn't what it claims to be, and explanations of other phenomena involving it are just wrong. I don't know why. So here we go.

There is no such thing as the overtone series. There is AN overtone series, but not THE overtone series, except in mathematics. That description makes a lot of sense to someone who has studied Fourier analysis and less sense to someone who hasn't, but it's worth a try. Pretend that there is a perfect string with constant density and infinitesimal width and that it has some finite length L and is held taut and fast at both ends. This is an idealization, remember. Now, pull the string in some shape with very small deviations from the resting state. Regardless of what that shape is, and this is the magic of it, you can write it as a sum of sine functions. This is called a Fourier decomposition, or a Fourier series. Those sine functions will look like your normal sine wave, but only those sine waves that have value 0 at the endpoints will be in the series -- so sin(pi*L), sin(2pi*L), sin(3pi*L), ..., sin(n*pi*L), for any integer n. For your perfect idealized string, the relationship between wavelength and frequency is such that if the whole string (sin(pi*L)) vibrates at a particular frequency (which depends only on the string's length, tension, and density), half the string (sin(2pi*L)) will vibrate at double the frequency, a third of the string (sin(3pi*L)) will vibrate at triple the frequency, and so on. So WHATEVER you do to the string at the start (assuming your stretching is very small), it will be vibrating in some weird pattern, but that weird pattern will be a sum of the frequencies of the whole string, half, one third, one fourth, and so on. If the whole string vibrates at a frequency of 64 Hz, after you make your weird initial condition, you will hear the 64 Hz, twice that (128 Hz), three times that (192 Hz), and so on. You'll actually hear all those notes. That is THE overtone series. It's described as C', C, G, c, e, g, bb, c', ..., with some exact pitches, where the G's are a little tiny bit sharp, the E's are somewhat flat, the Bb's are very flat, and so on, and authors make various claims as to its usefulness in various situations and as various explanations.

Of course, what I described is the perfect string. Real strings don't work like that, though they come close. Piano strings especially don't work like that, and if you look at them, you'll see that they aren't just plain strings, since piano makers try to correct those effects. The perfect string, where the overtones are integer multiples of the fundamental, is a linear medium. Real instruments aren't. The overtone series of a crotale, for instance, which is a round metallic pitched plate, is nothing like a string's -- since it's a circle, you can't break down a perturbation into sines; you have to use a different set of functions at different frequencies. Non-pitched instruments are even more nonlinear. Strings come close to being linear, but aren't exactly. Not even the human ear is exactly linear in its response. Vibrating air columns aren't. Reeds certainly aren't, and they respond differently at different frequencies.

This perfect string is used to describe the sounds that you hear from an instrument. An instrument produces, along with the fundamental that you hear clearly, a series of overtones at varying strengths. An oboe has strong overtones, for instance, which explains its rich sound, while the clarinet has weak ones, which explains it's dark quality. But since no instrument is really linear, this overtone series isn't exactly the one described. The set of frequencies sounded is called a spectrum, and it doesn't necessarily look like the overtone series described. It's just not perfectly in tune.

The overtone series is considered the basis of all everything. It's annoying, because, well, it isn't. Only the octave and fifth are actually important. The overtone third isn't the same third as the one in our triads, and this is obvious when we consider the minor triad -- it's not more dissonant than the major triad, but the minor third is much farther away from the "natural" third of the harmonic series. The third in our triads is, I believe, psychologically conditioned in us rather than an aural phenomenon like the octave and fifth. When those are in tune, mathematical cancellations in the sound waves (and the sound waves in the air themselves ARE linear, unlike the ones on the string) are audible, and the interval is perceived as "open". If the third is tuned correctly, it can also sound "open", and an in-tune major ninth can also sound "open". That is a DIFFERENT characteristic from tonal character. We can see from the scales of non-Western cultures that thirds can actually vary widely in pitch, and that major doesn't necessarily mean happy, and so on. The third isn't really a function of the overtone scale. The other notes aren't, either! At least not the way we do it. We take a fifth -- actually, something very close to the fifth -- and stack it repeatedly until we get to the original note (assuming everything is octave-reduced, of course), and THAT is what our system of harmony is based on, not the overtone series -- or rather, only indirectly the overtone series. Luckily, 3^12 = 531441 is very close to 2^19 = 524288, a difference of 1.36% (or 1.35%, depending on how you count it), so the perfect fifth needs to be fudged only a tiny bit to make it fit the octaves. There are twelve of them, so we get 12 evenly spaced tones in an octave, each therefore having a frequency of 2^(1/12) the previous pitch. This is NOT the overtone series! The overtone series does affect consonance and dissonance, to some extent, but only in the "beats" between notes of similar pitch -- play a C and a C#, and the waves will interfere and sound somewhat ugly. Play a C and a B, and it won't be so bad, but there will be beats between the B and the first overtone of C to create the dissonance. The dissonance can be hidden, say by playing C E G B, in which case the ear will hear a C major chord and an E minor chord rather than a strident major seventh interval. However, only the first few overtones (essentially up to the perfect fifth, not even so far as the "perfect" third) actually have this aural property to a reasonable strength. The higher terms in the overtone series are meaningless in this respect.

Finally, people try to say that the most stable voicings for chords have a spacing like that of the overtone series, wide at the bottom and tight at the top. THIS IS A CROCK OF BULLSHIT. The reason for this has nothing to do with the overtone series, except perhaps that some of the basic principles are the same. Two notes in the lower register are MUCH closer in frequency than the same two notes in a higher register due to the logarithmic nature of the scale. Two low C's are 32 Hz apart, from 32 Hz to 64 Hz, whereas two high C's are, say, 4096 Hz apart, from 4096 Hz to 8192 Hz. It's 8 octaves from the 32 Hz to the 8192 Hz, by the way. Part of the ear's pitch resolution is based on linear frequency, not the logarithm of it, which is what musical pitch is based on. This changes for the very high notes, of course, at the threshhold of hearing, but it's still very clear in, say, the piccolo range. So at the upper end of things, close pitches can be resolved by the ear much more easily than at the lower end of things. Furthermore, the overtone series DOES play a role, but it's only that part of the reason for the dissonance of low pitches is that the overtone series clash. They shouldn't clash much, but remember that the instruments are nonlinear, so they end up clashing quite a bit, especially on the piano. On a string or electric bass, which produces rather pure pitches, the clash is due to the bad resolution rather than the overtones, since the overtones are mostly absent.

OK, I think I've exhausted my rant. Feel free to disagree, of course.

A Scale! Ahava Rabbah!

http://en.wikipedia.org/wiki/Ahava_Rabbah

I'm a Jewish atheist, or Humanist, or Pastafarian, or whatever. I don't believe in gods, but I'm Jewish. Figure it out if you feel so inclined (Wikipedia can help). But the Ahava Rabbah scale is one of my favorite scales (mentioned in the last post as well), also known, according to the article linked above, as the Spanish phrygian, Jewish scale, Hungarian scale, or phrygian dominant. I'll stick with Ahava Rabbah, at least for now, but it really is a phrygian with raised 3rd.

I love this scale. I suppose the augmented second sounds "mystical", which in today's postpostmodern age is quite the cliche, but to me it really does. Listening to liturgical music that uses it makes me feel, well, elevated, which I'm sure the religious would interpret as "closer to Hashem". (This is because the religious can't write "Adonai", as that is using the name of God in vain -- instead, they use "Hashem", meaning "the name", in writing and singing, and they use "Adonai", "Lord", in actual prayer. They will sometimes use "Adoshem" when emphasis on pronunciation is necessary, and "Elokeinu" for "Eloheinu". Now you know.) The point is that I love this scale, and modulating to it is an interesting touch, much like that major chord in a minor piece that is like sunlight.

The typical cadences in Ahava Rabbah are not V-I as might be expected, since the 5 chord is actually vo rather than the v that you can change into a V. Instead, the cadences are bII-I and bvii-I (the convention is confusing and I can't be bothered to follow it; hopefully this is clearly referring to the chords on the 2 and 7 of this scale). bvii is especially nice, because since the important half step occurs between 3 and 4, an improvisatory-style melody would tend to hover around there, and the 7th degree would be a refreshing note to signal the cadence. In some chanting schemes this is actually done. A nice melodic cadence using bvii-I would be, in C: Bb' F E Db C; the Shabbat prayer Shalom Aleichem uses this, though the position of the tonal center makes this a half cadence instead. In fact, this is just the conventional phrygian cadence of Western tonal music, iv6-V, but with the function of an authentic cadence (and since this is used in mostly monophonic liturgical music anyway, with no attention to inversion numbers).

But yeah, Ahava Rabah, awesome scale.

Scales, Harmonic and Melodic

There are two similar but somewhat different things we call "scales", and sometimes those two things are different and sometimes the same. There is the harmonic scale and there is the melodic scale, and they are each sets of pitches from which one draws harmony and melody, respectively. The melodic scale is an ORDERED set of pitches, and the harmonic scale is not -- this is one of the main distinctions between them. This is important when we consider what the silly "common practice" people call the minor key.

It took me a while to realize that the three minor "scales", natural, harmonic, and melodic (and I don't mean the jazz melodic scale, I mean the CP one), were not all meant to be played. My first encounter with scales, as such, was in beginning band in sixth grade, or maybe in my piano computer program in fifth grade, and they were major. I knew what the minor keys were, but I never had to play minor scales. When I saw "harmonic minor" and "melodic minor" in a book from the school media center in sixth grade, or maybe someplace else, I saw them as curiosities, and I liked the sound of the harmonic minor scale, and I wondered at this melodic scale thing that goes up and down differently.

Eventually, in college, while taking a music theory course, I realized several things. First, the augmented second in the harmonic minor is essentially wrong. Second, the leading tone HAS to be a half step below the tonic, which is why the 7th is raised. Therefore, the 6th needs to be raised as well if you're moving to the raised 7th from below. So the minor key, with a flatted 7th and 6th, needs to be modified. The V chord has a leading tone when it goes to i, so it has to be V rather than v. Everything else still works, so the scale with this modification is the harmonic scale. The b6 and b7 still want to be used, but they can't be used if the tonic is approached by step from below. So if you're going to PLAY the scale, you have to raise the 6th and 7th on the way up, but going down you can keep the minor key feeling.

Personally, I find this all very silly, and enough other people find it silly, so we play just one minor scale: the melodic minor. When we play scales, which are a useful exercise for instrumental technique, the melodic minor should be played (if we are practicing for CP music), since those are the note patterns that we are likely to see. There is no reason to practice playing the harmonic minor scale -- this is because the harmonic minor scale was never meant to be played! The harmonic minor is the set of notes from which we draw the harmony. There are really only five chords, i, ii0, iv, V, VI, in the minor key (though with melodic minor melodic materials, you can include also ii and IV, but these are essentially chromatic alterations). III and VII don't really have functions so much, and even VI is a little iffy, so we can essentially limit ourselves to using the notes from the harmonic scale. The melody, conceived entirely separately and heard entirely separately (this is not true, but let's consider it as such), uses a different set of notes, and given the rules of CP, they are different going up from going down.

The melody and harmony, let me stress, use DIFFERENT SETS OF NOTES. There are plenty of examples, of course.

First, the blues scale. Mark Levine's Jazz Theory Book claims that nobody understands how it manages to work, but I claim that I do. (: In the key of C, the blues scale is C Eb F F#/Gb G Bb C. The twelve bar blues progression is C7 C7 C7 C7 F7 F7 C7 C7 G7 F7 C7 C7. Now, let's consider ripping the nonfuctional dominant 7ths out first, so we have C C C C F F C C G7 F C C. This uses the harmonic scale C D E F G A B, so we have that as a harmonic scale and C Eb F F#/Gb G Bb C as the melodic scale. The only common notes here are the tonic, subdominant, and dominant, the roots of the chords! We have here an extremely inflexible system, since this blues scale depends in a way on the fact that we're not using it freely but over a progression that essentially works like the traditional 12-bar blues. We can't really modulate in the scale; the scale has no symmetries! Of course, that's also true of the normal major scale; we have to introduce new notes to modulate. In this case, though, the tendency to the tonic is very strong from the Eb and the Bb. The Gb also tends very strongly down in a way that leads to the tonic. NONE OF THOSE THREE NOTES NEEDS TO BE IN TUNE. They aren't in the harmonic scale, and they form no harmonies. They can be wildly flat and they'll work just as well! (If C7 and F7 are used, though, the 7ths in those chords should probably be the same as the ones in the melody, since those are essentially melodic tones added to the chords rather than harmonic/functional ones).

The blues scale is essentially a harmony that works with bitonality over the C major harmonies in the progression. Let's see how the notes match up, ignoring common tones. Over a C chord, we have the Eb clashing with the E. The Eb has a strong melodic pull to the tonic, so you can hear it as an appoggiatura, essentially. The F clashes with the E as well, but that pulls to the Eb which pulls to the tonic. The Gb clashes with the G, but that pulls to the F which pulls to the Eb which pulls to the tonic. The F# pulls to the G, which is stable. The Bb pulls to the tonic or the fifth, but it doesn't actually clash with anything. The tonic essentially remains a pedal through the other chords, and the blues scale is essentially an elaboration of the tonic pedal. You can use the same logic to consider the notes over the other chords. Over F, then, you have C being stable as the fifth, Eb pulling down to it, F being stable as the tonic, Gb pulling down to it, F# not really working, G being the fifth of the pedal C blues scale, and Bb pulling the same as over the C chord in the tonic pedal scale. Over G7, C is the pedal, Eb tends to C in the pedal, F if the seventh, G is the root, F# tends to it, Gb tends down to the F, and the Bb tends either way in the pedal. So the clashes aren't really clashes because the harmony and the melody are heard separately.

Another example are the modes of the harmonic minor scale, taken melodically. The interesting ones in Jewish music are phrygian #3, dorian #4, and aeolian #7 (the original harmonic minor); they have names in Hebrew that I don't remember. The others (locrian #6, ionian #5, lydian #2, and, uh, mixolydian #1 which is really weird) don't have very useful corresponding harmonic scales, that is, the melody notes can't really be used to form harmonies very easily. You could make a doubly "harmonic" scale as well by taking a phrygian #3#7 or an aeolian #4#7. In these cases, the augmented second is a characteristic interval, though it doesn't have to be -- it might well be treated as a leap rather than a step.

The phrygian #3 scale in particular is a MAJOR scale. The tonic chord is major! The harmonic scale for it is certainly phrygian #3, but the melodic scale isn't, if you don't like augmented seconds. It's just as well to raise the 2nd going up and lower the 3rd coming down if it makes sense in the music when stepwise motion is called for. Of course, a solution is to avoid stepwise motion in that direction, never going lower than the raised 3rd in a scalar passage or higher than the 2nd, and leaping across the gap when necessary. An example from Fiddler on the Roof, "If I were a rich man", in C: G F G F E, C. E F G F G F E F G A Bb A Bb A G. This is a somewhat bad example because it isn't really in this mode, but see how it just avoids the Db or D altogether? This is actually mixolydian (which is another Jewish mode as well), of course. A better example, still from Fiddler on the Roof (it's really the easiest source for this, even though it's not particularly authentic), is the fathers' theme in "Tradition", also here in C: C CDE F GF#GAbG E FEFGF Db ED#EFE G C CDE F GF#GAbG EFEFGF Db C. In this case the majorness and the Db are very clear. There is one occasion of Db going to E, but it's certainly as a leap rather than a scale. When E has to be approached by step from below, the passing tone is D, not Db, but when the harmony is a bII Db chord (or a bvii Bbm chord), the Db is necessary. This way you can have music in the mode that still has smooth voice leading.

And so it is that harmonic and melodic scales are not only different notes but different things altogether. Comments?