Author Topic: Tuning in Fifths: The Hairy Details  (Read 323 times)

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Offline MayorThird

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Tuning in Fifths: The Hairy Details
« on: March 01, 2022, 07:02:13 AM »
As promised, this is the more in-depth discussion of the fifths tuning from my recent post Tuning in Fifths[1].

Let us consider a hypothetical 24-hole ring shaped harmonica tuned in fifths, i.e. going beyond hole 24 we end up where we started.  Look at the key table and observe how each row contains two circles of fifths interspersed such that it forms a sequence of triads in all keys.


|    | 1     | 2     | 3     | 4     | 5  | 6  | 7  | 8  | 9  | 10 | 11 | 12 | 13    | 14    | 15    | 16    | 17    | 18    | 19 | 20 | 21 | 22 | 23    | 24    |
|----+-------+-------+-------+-------+----+----+----+----+----+----+----+----+-------+-------+-------+-------+-------+-------+----+----+----+----+-------+-------|
| b  | C     | E     | G     | B     | D  | F# | A  | C# | E  | G# | B  | D# | F#/Gb | A#/Bb | C#/Db | F     | Ab    | C     | Eb | G  | Bb | D  | F     | A     |
| b* | C#/Db | F     | Ab    | C     | Eb | G  | Bb | D  | F  | A  | C  | E  | G     | B     | D     | F#    | A     | C#    | E  | G# | B  | D# | F#/Gb | A#/Bb |
| d  | D     | F     | A     | C     | E  | G  | B  | D  | F# | A  | C# | E  | G#    | B     | D#    | F#/Gb | A#/Bb | C#/Db | F  | Ab | C  | Eb | G     | Bb    |
| d* | D#    | F#/Gb | A#/Bb | C#/Db | F  | Ab | C  | Eb | G  | Bb | D  | F  | A     | C     | E     | G     | B     | D     | F# | A  | C# | E  | G#    | B     |


Recall that for solo tuning each key requires a different blow/draw/button pattern (so there are twelve patterns to learn) whereas for diminished or augmented tuning you only need to learn three or four patterns, respectively.  For the tuning in fifths it's a bit different because you technically don't learn different patterns for different keys but there is one large pattern spanning seven octaves, i.e. one round of the hypothetical 24-hole ring-shaped harmonica.

And here is the master pattern.  Xs are the notes to play and Os are the choice notes.  Columns with 1 in the header row represent odd-numbered holes and columns with 0 represent even-numbered holes.


|    | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
|----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---|
| b  | X | X | X | X | X |   | X |   | X |   | X |   |   |   |   | X |   | X |   | X |   | X | X | X |
| b* |   | O |   | O |   | O |   | O | X | O | X | O | X | O | X |   | X |   | X |   | X |   |   |   |
| d  | X | O | X | O | X | O | X | O |   | O |   | O |   | O |   |   |   |   | X |   | X |   | X |   |
| d* |   |   |   |   | X |   | X |   | X |   | X | X | X | X | X | X | X | X |   | X |   | X |   | X |


Align this pattern with the key table above.  Shift to the left or right by your hearts content.  As long as the 1-columns are aligned with odd-numbered columns, the pattern table now marks all the notes that are natural to the major scale of the key from the key table that is aligned with the top-left cell of the pattern table.

Try it!  Choose any key you you'll find that the above table shows exactly the notes of the corresponding major scale if you start the pattern on the non-slider blow-reed that produces your chosen pitch.  For example, for C major start the pattern on hole 1.  For A major start the pattern on hole 7.  For Db major start the pattern from hole 15.  Don't forget that that our harmonica is ring shaped and the hole to the right of 24 is hole 1.

But of course you can play scales from anywhere on the harmonica—you don't have to start on an odd-numbered blow-reed.  To this end I will mark all the root notes on the master pattern for the maJor scale with J1–J7.  That means playing the Xs and the markers between J1 and J2 yields a major scale, as well as for J2 and J3, J3 and J4, and so on.  Remember that the numbers in the header row only denote if the hole is even- or odd-numbered.  For readability, I have visually separated blow and draw reeds and removed choice notes.


|    | 1  | 0 | 1 | 0  | 1 | 0 | 1  | 0 | 1 | 0 | 1  | 0 | 1 | 0  | 1 | 0 | 1 | 0  | 1 | 0 | 1  | 0 | 1 | 0 |
|----+----+---+---+----+---+---+----+---+---+---+----+---+---+----+---+---+---+----+---+---+----+---+---+---|
| b  | J1 | X | X | X  | X |   | X  |   | X |   | X  |   |   |    |   | X |   | J6 |   | X |    | X | X | X |
| b* |    |   |   |    |   |   |    |   | X |   | J4 | X | X | X  | X |   | X |    | X |   | X  |   |   |   |
|----+----+---+---+----+---+---+----+---+---+---+----+---+---+----+---+---+---+----+---+---+----+---+---+---|
| d  | X  | X | X | J2 | X | X | X  | X |   | X |    |   |   |    |   |   |   |    | X |   | J7 |   | X |   |
| d* |    |   |   |    | X |   | J3 |   | X |   | X  | X | X | J5 | X | X | X | X  |   | X |    | X |   | X |


We can now clearly see that the master pattern contains seven octaves that are played slightly differently.  The octaves starting from J1 and J4 seem very comfortable to play, those starting from J5, J6 and J7 occasionally require using the slider and only octaves starting from J2 and J3 seem slightly less comfortable as you will need to flatten some blow notes to the previous draw* note and draw notes to the previous blow* note.

Here is one really dense way to visualise the master pattern.  We can omit blow/draw/slider information because the pattern advances in half and whole steps only.  However, I'll have to mark one sign with odd so we know where odd-numbered holes are.  Again, the pattern is infinite and wraps around:


| odd+ - + +*/- + - + +*/- + - -* +*/- + - -* +*/- + +* -* +*/- + +* -* +*/- -* +* -* +*/- -* +* -* + -* +* -* + -* +* - + -* +* - + -* + - + -* |


I'm repeating myself but this is the pattern that you will use for every key and every mode (major/ionian, minor/aeolian, dorian,…).  It is all just a matter of defining the root of your scale.  Play this pattern starting on blow-reed 3 to get G major.  If you start on this reed and start the pattern from the twelfth note (i.e. shifted to the left by twelve steps), then you will get G minor.

Now let's contrast this tuning to other more or less established tunings.  First, I would like to compare it to diminished and augmented tuning.  These two are super interesting because they are highly key-agnostic.  For solo or classical tuning each of the 12 keys is different and requires a different pattern.  Not so with dim./aug. tunings!  Here, each row in the key table is a sequence of thirds (always minor for dim. and major for aug.), which makes the interval spacing in the instrument perfectly even.  Because a minor third consists of 3 half steps and 3 is a factor of 12, the diminished-tuned harmonica partitions our 12 keys into 3 groups of 4 keys and the keys of such a group use the same pattern, e.g. C and Eb major.  The case for augmented tuning is perfectly analogous.  That means you will have to learn 3 or 4 patterns to play in any key on the dim. or aug. tuned harmonica, respectively.  Also, different octaves of the same key use the same pattern.  On the downside you have that playing scales is a bit less intuitive because we tend to think in steps.  Just think of playing C major on a C classical-tuned harmonica, which is perfectly intuitive and flowing.  On dim./aug. harmonicas, you will always have to use double blows or draws with the slider just to play C major.  Personally, I would say this is a worthy trade-off compared to the downsides of solo or classical tuning.  And finally, you can only play diminished (seventh) and augmented chords on these instruments.  Having all diminished chords is definitely pretty useful but only have augmented chords is… let's say very jazzy.  But the intricacies of these tunings is not the focus of this post.

If you tune in fifths, the situation is different.  A fifth is 7 half steps and not a factor of 12.  That means if you stack fifths, you will reach every key until you end up on the starting key again.  If you play the same key an octave apart, they will require a different direction of breath and/or use of the slider.  But the situation for stringed instruments is analogous and no one is complaining about that ;D. The upside is that you can play a hole lot of different chords and you can play perfectly natural feeling scales.  The most interesting thing I would say is that this instrument is truly key agnostic (at least this hypothetical ring-shaped 24-hole harmonica is, as I will touch on below).  Playing any scale around the whole instrument will always require the same pattern regardless of key.  Yes, the pattern spans seven octaves whereas with diminished or augmented tuning you only need three or four, respectively, one-octave patterns.  But what tuning in fifths points out is that the relationship between notes, i.e. intervals, is what truly matters (unless you have perfect pitch) and not the key.  They are all the same!  Stop segregation! ;)

OK, so that was fun!  But I think it's time to get real for a second.  Up until now the whole discussing has been entirely hypothetical.

  • No one has a ring-shaped 24-hole chromatic harmonica (where would the button even be?).  If we restrict ourselves to actual straight harmonicas with 12–16 holes, we will lose some of the shift-to-transpose properties.
  • While it is possible to disregard octaves for most theoretical considerations, you cannot do that in practise.  If you want to transpose from C to D and shift by two fifths (4 holes) you'll be a second and and octave higher.  Unless you're OK with that, instead of playing from J1 starting on blow 1, you'd have to play from J7 starting on draw 1.
  • You can't play octaves.  For me personally though, that's not a problem at all.
  • All octaves are different.  I know this sounds like a minor catastrophe but what you gain is that every key follows the same seven-octave pattern.  So instead of having to learn twelve different patterns for 12 different keys, you only have to learn seven (or one really long one).
  • While you can play all major and minor triads as well as major seventh and minor seventh chords on a 14-hole harmonica tuned in fifths, some are restricted to the really high or really low end.  On a 12-hole harmonica, you'll lose the chords B major, B major seventh and Ab minor seventh if I looked carefully enough.

To wrap up, is this the best tuning ever?  Obviously that depends on the use case and for some it is definitely not.  But if you want to play cello or violin repertoire, this might actually be worth a try!  After I have decided on which model to get, I will order such instrument from Seydel and see for myself.  If I have made any mistakes in this in-depth view, feel free to point them out so we can discuss them.  I'm sorry for the long post and I hope it wasn't too confusing.  Thanks for reading! ;D

1 https://forums.SlideMeister.com/index.php?topic=20764.0

PS: If the tables horizontally don't fit onto your screen, just zoom out.  Usually that can be done by holding CTRL and using the scroll wheel.