Some further information about the LUNA Scales.

 

Why the Luna is tuned in its own scales, and whats the difference to common handpan scales?

 

About the perfect just intonation as given fom the natural overtone series, wich the Luna tuned in.

 

About the Dominant or Subdominant Ding, what it is and whats special about its use ?

 

Why the Luna is tuned in its own scales.

Why only 12-core scales?

 

 

There are several reasons for this.

 

First of all, it is a response to the growing confusion surrounding Handpan scales.

The feedback I get from customers who often have big problems finding and choosing their scale reflects this confusion.

 

Many people without a background in music theory lose themselves in the multitude of different scale designations and sound models,

and even among handpan manufacturers there are many who have no deeper understanding of the type of scales, their designation, interval structure and musical modes.

 

In the past, for example, tuning was often done according to lists of notes, scales of certain manufacturers were copied, and small changes such as omitting a note were given a different name, so that there are now two different names for the same tuning, which can then differ from manufacturer to manufacturer in their division - in short: a right mess.

 

In addition, most Handpan names have no relation to their characteristics, neither in the music-theoretical sense, nor in the figurative "atmospheric" sense.

 

For example, the name "C-Amara" simply doesn't say anything about the mood, neither that it is an Aeolian minor in music theory, with classical minor third, nor that it creates a slightly melancholic but nevertheless balanced mystical atmosphere or energy.

 

The reduction to the 12 LUNA core scales is therefore the attempt to bring the different scales back to their roots - to create less, but more distinguishable and characteristic moods for the Luna.

 

If you are faced with the great challenge of having to choose a Handpan Scale, you can overcome a great hurdle by first sorting out the double "twin tunings" or very similar tunings in order to drastically reduce the sheer mass.

 

For example, there is no difference between a "C-Amara" and a "minor Celtic".

Both come from the same core family (music theoretically aeolian minor) with the same interval structure, defined by a minor third & minor sixth, with perfect fourth and of course fifth.

 

There is also no great difference between these two and the so-called "Magic Voyager", except that one note has been omitted, namely the fourth.

 

Omitting a note or moving the scale start and end points creates a variation of the scale and can shift the focus more to certain intervals, but does not create a completely new mood with a completely different character.

 

This applies to a large number of scales, such as "Kurd" "Integral" "Enigma" and many others.

 

So the main reason for the LUNA tunings is to return all these hundreds of scales to their musical main roots in order to get fewer scales which differ very clearly in their main character.

 

This leads to a smaller but clearer range of scales, the 8 LUNA scales.

 

 

 

Another reason for the LUNA tunings is the sound quality. The LUNA tunings are all specially developed for the LUNA, the shell geometry, size, material and tuning style are all variables that influence the choice of scale, placement of start intervals, etc. The LUNA tunings are all designed for the LUNA, and the LUNA tuning is based on the LUNA scale.

 

You can't (or shouldn't) simply adopt a certain scale as it appears on a Handpan of any manufacturer and transfer it 1:1 to your own Handpan without deeper consideration.

 

 

  What does Nana, Roku & Go mean?

 

 

 

These are the Japanese numbers. Nana = 7, Roku = 6, Go = 5.

They denote the 3 subspecies of each LUNA Scale, their full heptatonic, hexatonic and pentatonic.

 

 

Although there are only 8 LUNA core scales, each of them can occur in one of these 3 variations:

 

 

1st Nana, Heptatonic

 

Hepta - of seven, means that there are 7 notes before the octave step.

 

This is the entire scale range with all intervals, which offers the greatest acoustic vocabulary of expression and is good if you want to keep the scale as flexible as possible. Nana scales offer the most possibilities of interval combination.

 

2nd Roku, Hexatonic

 

Hexa - of six, means that there are 6 notes before the octave step.

 

This scale omits one of the interval steps in favor of rising one note higher, above the first octave level. Which note is omitted depends on the interval structure of the tuning and is chosen so that the defining "core" intervals are preserved to preserve the unique character of the scale.

Roku scales are the most balanced between flexibility and harmony, offering a beautiful range between high and low notes.

 

3rd Go, Pentatonic

 

Penta - of five, means that there are five notes before the octave step.

 

In this scale, two interval steps have been omitted to create a unique and characteristic pentatonic, in which only the most characteristic interval steps remain. Pentatonics are widespread in Asia, e.g. in traditional Chinese or Japanese music, and are therefore often associated with an Asian energy.

 

Go scales are the most harmonic and intuitive that one can play.

With only five different tones up to the octave step, they are more limited in their acoustic vocabulary, in the form of interval combinations, compared to heptatonics and hexatonics, however, on the other hand they also possess the largest range between lowest and highest tones, the "widest space between heaven and earth".

 

 

Are the LUNA moods something new that you have invented?

 

 

No.

 

Most of them are neither new nor invented, although some have been modulated in such a way that they can be built with the highest possible sound quality on the LUNA.

 

In fact the LUNA tunings are mostly very old tunings, as you can find in the ancient Greek modes, (Tonai) as for example, Aeolian ("typical D minor", "Kurd", "enigma" etc.) Lydian, Ionian Phrygian etc..

 

A large part of the LUNA scales, however, are not to be found in the European music culture, but come from the Japanese / Chinese, like the "Ma Hô" and the "In Me" as they are used for example in the Chinese Gu Zheng music of the great musician 許嫚烜.

 

So the LUNA Scales are nothing new.

They are mostly well-known musical modes/scales from Asia and Europe.

 

 

 

Then why don't you name the European LUNA scale with the Greek names, e.g. "Aeolian" or "Lydian" ?

Why the Japanese names?

 

 

 

First: because there are Japanese equivalents for many European modes. For example, Phrygian is found in the well-known Japanese Akebono.

 

Secondly: because Asian Japanese or Chinese scales are never defined and bound by a certain keynote such as C or F.

This is due to the completely different kind of music theory and our European fixation on the chromatic scale.

 

And the 8 LUNA scales are therefore not bound to a special tonic, so that, for example, the "Yu Mei" can be built on any tonic or any fundamental frequency (within the technical limits) with the same scale.

 

Third: Because both Asian scales and LUNA scales are tuned in perfect, pure intonation, as derived from the natural overtone series.

 

This is the most natural and mathematically perfect way of tuning.

 

Thus the interval ratio for the major third is, for example, 5/4 or 9/5 for the major sixth, which would not apply to the European scales.

 

It makes more sense to use the Asian names, which already imply the pure tuning.

 

The final reason for this is that not everyone who wants to play the Handpan is a music theoretically trained musician, and some have probably never heard of harmonic music theory, intervals, or pure tuning and mid-tone temperament.

 

This is also absolutely not necessary to play the LUNA.

 

So for these people terms like "Aeolian minor" or "Phrygian mode" are not much help to orientate oneself - but a descriptive association of the scale can convey a certain "feeling" for the atmosphere the scale can create.

 

Therefore, it can be very helpful to have a meaning name that can provide some associations to the scale.

 

The naming of the LUNA scales themselves is a kind of description and provides some of this emotional and descriptive information.

Perfect just intonation as derived from the natural overtone-Series

One of the main features of the LUNA scales is the use of pure intonation as opposed to the most commonly used modern midrange temperament.

 

 

This ensures that all intervals are tuned very clearly and purely and the internal resonance is significantly increased.

 

Although I will try to keep the explanation simple, we will have to dive a little into music theory to fully understand this:

 

First of all, we have to understand that scales are never defined by notes - they are defined by a certain combination of interval steps (which can then be represented by notes).

 

So what is an interval?

 

Well, let's pick any frequency as a fundamental - just imagine a plain string, like a guitar string or another. It doesn't matter how long this string is, but for simplicity's sake we assume it's 1 meter long.

 

So this is our basic frequency - or the tonic of our scale.

Imagine now, we take a finger and pluck this string - it will start to vibrate as follows (in reality it vibrates in many more ways, but these are irrelevant to us at first) and emit a tone.

 

Our fundamental - let's say it is a C3.

We can now define this frequency in a simple mathematical term as 1 or - we will need this later - as a ratio of 1/1 equal to 1.

Based on this, we now create our first interval step, which is one of the most important: the octave.

The octave sounds like exactly the same note - but a "step" above our foundation, and it has twice the vibration frequency as our fundamental.

 

On our string, the octave would fibrillate so and can be mathematically defined as the double frequency, tso 2 ( 2x1) or the ratio: 2/1

So now we have our base frequency, with the ratio 1/1, of which we said it was C3 (but it could be any other note) and we have our octave, which is the ratio 2/1 and thus a C4.

These are the limits within which we create a scale. Everything that goes above or below these octaves is just a repetition that we don't have to worry about now.

So let us take the second most important interval, which is the fifth.

The fifth is perceived as a very pleasant interval step and is so important that the entire Western 12-note system is based on it, namely on the quint-layering.

On our string, the fifth would vibrate as follows:

To make the fifth sound, we would have to shorten our string, for example, like a guitar player shortens a string when he picks it off with his finger.

This should be done in the ratio 3/2, which is the ratio of the pure fifth:

In our example of the C3, the fifth with the ratio 3/2 would be G4.
Starting from here, the chromatic scale of Western music was constructed, which places fifths on fifths.

So let's start from C and look for the fifth of it, the G.
If we repeat this step and look for the fifth to the G, we come to the D.
 On the keyboard of the piano, we always move 7 semitones to the right.

 We can also calculate the ratio of this D.
This is done simply by multiplying the G -> 3/2 by another fifth step, i.e. 3/2, and then going an octave lower.

It looks like this:

3/2 x 3/2 = 9/4

Now that we have exceeded the octave point, however, we must lower the result by one octave so that we are again within the correct octave and thus receive the D as the second after the C.

For this we have to divide the result by the ratio of the octave we said to be 2/1:

 9/4: 2/1 = 9/4 x 1/2 = 9/8

The perfect D, as derived from the quint layering, would therefore have a ratio of 9/8.

In our drawing its oscillation would look like this:

And here is how those frequencys would vibrate differently on our string:

 

the tonic - octave - fifth - the second ( wich we calculated as fifth from the fifth )

Now that we understand this, we can see how the 12 notes are created in Western music - they are all created as a fifth from the fifth from the fifth from the fifth from the fifth.... here is the complete series of fifths that begins with C, followed by the fifth of C = G followed by the fifth of G = D etc..

 

C -> G -> D -> D -> D -> A -> E -> E -> B -> Gb -> Db -> Ab -> Eb -> Eb -> Bb -> F -> C

 

That is why European music has 12 notes, because after 12 such operations you reach FAST - but only almost - the opening note, the C.

 

And this is where the problem and the various attempts to solve it, such as the mid-tone temperament, begin.

 

 Mathematically speaking, the multiplication of fifths is always a multiple of 3/2.

Or, if we want to represent the ratio as a decimal number: 3/2 = 1.5 multiples of 1.5.

 

So we have multiples of 1.5 which we can also write as a superscript 1.5^2 ( 1.5 x 1.5).

 

The core problem is that we calculate with the ratio 2/1, i.e. with multiples of 2 ( 2^2 ; 2^3 ; 2^4 etc.) in order to get perfect octaves.

 But unfortunately these two never fit together perfectly.

 

You can demonstrate this by looking at where a multiplication in octave steps ends after a complete octave:

 

Namely after 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2^7 (because we created 7 whole tones between one octave) = 128

 

And here ends the series of multiples of 1.5 ( thus the quint layering ) after 12 steps ( since we produce 12 semitones ):

 

1,5 x 1,5 x 1,5 x 1,5 x 1,5 x 1,5 x 1,5 x 1,5 x 1,5 x 1,5 x 1,5 x 1,5 x 1,5 = 1,5 ^12 = 129,75

 

So we have the result 128 once and 129.75 once.

 

 

 

As we can see, perfect octaves can never be matched with perfect fifths or interval steps. It seems that we have to decide... perfect octave or perfect intervals...

 

 

 

What are the solutions?

 

Well, great thinkers have been thinking about it for centuries, starting with one of the first, Pythagoras, but also Kirnberger, Bach and many other musicians and composers have developed their own suggestions and methods to solve this problem.

 

At the moment we will not go into these like e.g. the Pythagorean tuning or others.

 

Suffice it to say that there are hundreds of different temperaments and tuning methods. ( Alone in Europe - not to mention completely different methods in different cultures! )

 

The most common type of tuning today to deal with this problem is the so-called mid-tone tempering, which is also the widespread standard for Handpans.

 

We have seen that we end with multiples of perfect fifths at 129.75, while the perfect octave ends at 128.

 

The difference between these two is the so-called "Pythagorean comma" which is calculated as follows: 129.75 - 128 = 1.75

 

This difference would produce an audible dissonance in the last interval step, or - with perfect intervals - make the octave appear clearly too high.

 

The mid-tone tempering deals with this problem as follows:

 

We take the Pythagorean comma - 1.75 and divide it by 12 - because we have 12 interval steps - and then distribute this error evenly over all intervals.

 

So 1.75 : 12 = 0.145 on each of the 12 interval steps to achieve a perfect octave.

 

This means, for example, if the perfect ratio of e.g. a fifth is 3/2 = 1.5 in the pure tuning.

then it is now 1,645 in the mid-tone temperament.

 

A mid-tone fifth is therefore slightly higher and slightly out of tune, in contrast to a pure, perfect fifth.

 

Another example based on the fourth:

 

The ratio of a perfect fourth 4/3 = 1,333

The ratio of a mid-tone quarter = 1.478

 

To sum up: The Western mid-tone temperament has only one single, truly natural and pure interval, the octave.

All other intervals must be somewhat impure and out of tune to fit the octave at the end.

Even if the difference seems to be tiny (e.g. from 1.5 to 1.645 for the fifth), it is perceptible to an experienced ear and gives the intervals and especially the chords a restless, impure quality.

 

 

So far so good. But if the LUNA is tuned purely, then it doesn't fit the octave at the end, does it?

 

No.

 

The LUNA contains perfect natural octaves in a 2/1 ratio, just like the mid-tone temperament, AND has the perfect intervals in perfect natural ratios, like 3/2 - 4/3 etc.

 

Since the Handpan is not a chromatic instrument with all 12 semitones, it opens up a special possibility for pure tuning.

 

For every LUNA tuning there is a certain mathematical calculation in which the "error interval", also called "Wolf's fifth", is mathematically "compressed" and calculated into a note that simply does not occur in the respective scale!

 

The mathematical error, the non-matching of fifth and octave multiples is shifted until it comes to rest in an interval that does not exist on the instrument.

 

This must be calculated individually for each individual scale on the LUNA tuning list.

 

The Asian names of the LUNA are chosen because they all imply pure tuning, which has been widely used in Asian cultures that do not use chromatic scales for a very long time.

 

Again summarized in a few words: All LUNA scales are in pure, natural, perfect intonation. They have both perfect interval steps and perfect octaves, because the Pythagorean comma is calculated for each individual scale so that it does not appear on the instrument.

 

It is not just a mathematical gimmick, because the pure tuning is also naturally perceived by the ear as pure tuning, compared e.g. with the mid-tone temperament.

 

This is the most natural and cleanest tuning possible in the non-chromatic range.

 

 

 

 

Subdominant or dominant Ding and full range of Scale

The DING ( central tone field ) is always dominant or subdominantly tuned at the LUNA.

 

 

1. subdominant Ding.

This means that the Ding is the fifth of the fundamental ( tonic ), but an octave lower - for a G3 as fundamental the D4 is the dominant ( fifth ) - subdominant would then be a D3.

 

2. dominant Ding.

A dominant Ding means that the tonic of the scale is the fifth of the Ding. ( Or in other words, the Ding is the fourth of the fundamental. )

That would be the C3 for a G3. ( Since G3 is the fifth of C3. )

 

 

 

What are the differences between subdominant, dominant and a Ding tuned as a fundamental?

 

 

While the Ding in most other Handpans is the tonic, i.e. the fundamental, all LUNA tunings are formed with dominant and subdominant Ding

 

Why?

 

The typical tuning of the Ding as the fundamental of the instrument is, for example, a C3 Ding for a C-scale, e.g. the C-Amara.

 

This reflects the typical playing style for Handpans that has evolved and established over the years, and which focuses heavily on percussive patterns.

 

As the Handpan became available to a wider public, it attracted many people with percussive backgrounds, drummers, Darbouka players and other percussionists.

 

They took what they brought from their percussive background and applied it to the Handpan.

The result was a way of playing that is largely focused on percussive patterns, which is a possible way of dealing with this instrument and should not be criticized here, but which is not the only way to access this instrument.

 

It is only natural that from this perspective the Ding plays a very dominant and important role in the playing technique of most Handpan players, while the choir (the notes in the ring) plays a somewhat subordinate role and is often used only in the way to fill the rhythmic patterns.

 

The LUNA, however, was conceived from its beginnings as a more melodic instrument with a much more "feminine" character.

 

For an instrument with this focus, however, the key tuned Ding does not make sense for the following reasons:

 

The main problem with this is that on most fundamental Ding scales the first tone field of the instrument is NOT the fundamental of the scale.

 

With a tonic Ding, the scale usually begins somewhere in the middle, usually the 3rd or 4th, sometimes even higher tone field.

 

This results in a divided scale where the lower part is not complete and is shifted to the upper part above the octave. This makes it impossible to play complete melodies in this scale because the scale is simply not completely available between an octave level.

 

As a result, tonic Ding scales can be named in a particular musical mode, but can practically not be played melodically in that key, leading to great confusion.

 

This inability to play complete melodies in this mode is, in my opinion, one of the main reasons for stimulating a strongly thing-centered, percussive style of playing, with more or less hard beats and repeated beats on the Ding accompanied only by a few melodic accents.

 

This is the Handpan's current direction of development.

 

A subdominant or dominant Ding, on the other hand, offers a complete scale from the first tonal field with tonic to the last with octave, inviting a much more melodic approach to the instrument.

 

Depending on the interval structure of the scale, dominant and subdominant things have very different influences on the whole scale and can be used powerfully to emphasize the overall atmosphere and energy of a scale while allowing enough space for modal shifts.

 

In summary, while providing a definite rest center, both dominant and subdominant things inspire the player to focus more on the choir and melodic playing, as opposed to a typical percussive ding-centric playing that is more promoted by key tuned Ding instruments.

 

 

 

LUNA's aim is to offer the best possible combination of aesthetics and musical possibilities.

 

It is therefore built exclusively with a central note and 8 tone fields. No mutants, no 10 or 11 notes, no bottom-notes.

 

For me personally and from an aesthetic point of view, the Handpan in this format is at the height of elegance.

You can't add anything to it without taking away something of its minimalist form and elegance.

 

This is not to say that mutants, bottom notes and other things are bad, there have been some LUNAE with such additional developments in the past, but it is not what I want to develop further.

 

Instead of adding more and new, the Luna is an attempt to use my energy to see how far this simple elegance can be refined, polished and perfected.

 

This decision also influences the choice of the tuning of the Ding - because if the fundamental is on the first tonefield and not on the Ding, this very fact gives the whole Handpan another layer of playing opportunity, which is very important if you are limited to a central tone field and 8 more tone fields.

 

In some scales, you also get an additional note from the fifth of the Ding tone field, which is not necessarily in the choir, so you get the maximum possible musical expression in the most elegant and minimal design - the goal of the LUNA.