THE OPTIMAL TUNING FOR ALL TYPES OF MUSIC? THE ADVANTAGES OF THE IONIAN MODE CIRCULAR TUNING

Anything apart from the two mainstream default harmonicas (Solo-tuned fully-valved chromatic, and un-valved Richter 10-hole diatonic). Alternate tunings, different construction, new functionality, interesting old designs, wishful-thinking... whatever!
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drkcostas
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Re: THE OPTIMAL TUNING FOR ALL TYPES OF MUSIC? THE ADVANTAGES OF THE IONIAN MODE CIRCULAR TUNING

Post by drkcostas » Wed Jan 15, 2020 6:37 pm

DIATONIC GENDRE: CIRCULAR TUNING FOR THE 6-NOTES CELTIC MINOR SCALE
We may also notice that the 6-notes scales are favored for a harmonica, as the periodicity in the circular tuning is per octave and not per 2 octaves as in 7-notes scales. A good example is the Celtic minor 6-notes scale ( in semitones 2-2-3-2-2-1). This scale is used also for the hundpans and hang drums. The example is in the next table of tunning for the case of D root. The blow row is only the chord I and the draw row only the chord ii. The Celtic minor is the maximal harmonic 6-notes scale, in the sense that it is a 6-notes scale with the maximum number of standard chords. In the same way that a 7-notes diatonic scale is a maximal harmonic 7-notes scale in the sense that it is a 7-notes scale with a maximum number of standard chords (see the article https://simplerguitarlearning.blogspot. ... e-and.html )
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Celtic_D_minor.gif
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Re: THE OPTIMAL TUNING FOR ALL TYPES OF MUSIC? THE ADVANTAGES OF THE IONIAN MODE CIRCULAR TUNING

Post by EdvinW » Wed Jan 15, 2020 10:23 pm

The
drkcostas wrote:
Wed Jan 15, 2020 6:37 pm
CIRCULAR TUNING FOR THE 6-NOTES CELTIC MINOR SCALE
We may also notice that the 6-notes scales are favored for a harmonica, as the periodicity in the circular tuning is per octave and not per 2 octaves as in 7-notes scales. A good example is the Celtic minor 6-notes scale ( in semitones 2-2-3-2-2-1). This scale is used also for the hundpans and hang drums. The example is in the next table of tunning for the case of D root. The blow row is only the chord I and the draw row only the chord ii. The Celtic minor is the maximal harmonic 6-notes scale, in the sense that it is a 6-notes scale with the maximum number of standard chords. In the same way that a 7-notes diatonic scale is a maximal harmonic 7-notes scale in the sense that it is a 7-notes scale with a maximum number of standard chords (see the article https://simplerguitarlearning.blogspot. ... e-and.html )
I'm a bit late with this, but welcome to the forum!

The tuning you describe is known as extended Paddy Richter, and it's a shifted version of what's know as the EDharmonica tuning, see for instance https://edharmonica.com/

You talk of a Celtic minor scale, but if D is the root of the scale it's rather a major scale. Also, the seminote pattern describes a major scale with missing fourth. The tuning you present is fairly popular for minor playing, but with B used as the root.
Edvin Wedin

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Re: THE OPTIMAL TUNING FOR ALL TYPES OF MUSIC? THE ADVANTAGES OF THE IONIAN MODE CIRCULAR TUNING

Post by drkcostas » Thu Jan 16, 2020 10:02 pm

DIATONIC GENDRE.
Thank you for mentioning it. I was not aware of the EDHarmonica neither of the extended paddy Richter tuning. In the terminology that I am used in music , a scale is a sequence of notes AND ALL CYCLIC PERMUTATIONS of it, so as to differentiate it from the mode which is only in a particular sequence . So e.g. the C D E F G A B C is a diatonic scale (and Ionian mode) with root C , and the A B C D E F G A is not a different scale (e.g. A minor) but a different mode , the Aeolian mode. So there is no C major scale and A minor scale but only major and minor modes , or C Ionian mode of the C diatonic scale and A Aeolian mode of the C-diatonic scale. The Celtic minor is a fairly well known scale in handpans , and the name Celtic probably signifies centuries older use. See e.g. https://metalsounds-shop.com/en/steel-t ... ticks.html where the A C D E F G A is refered as the Celtic minor with semitones intervals 3-2-2-1-2-2. But I have not find anywhere else the term Celtic for this 6-notes scale. The Wikipedia mentions the A C D E F G (3-2-2-1-2-2) simply as Hexatonic scale here https://en.wikipedia.org/wiki/Hexatonic_scale . Thus all cyclic permutations of 3-2-2-1-2-2, like 2-2-1-2-2-3 , 2-1-2-2-3-2 (as in EDharmonica) , 1-2-2-3-2-2 .....2-2-3-2-2-1 are all the same scale (Celtic minor) in different modes . That is why I mentioned it as Celtic minor. The scale of the EDharmonica has interval structure 2-1-2-2-3-2, could be therefore called 3rd mode of the Celtic minor, while the scale that I used in the D -roor diatonic scale in my previous post is the 5th mode of the Celtic minor. Or if we drop the adjective minor (so as to refer it to only a particular mode of it, the 3-2-2-1-2-2) then we could simply say 6-notes Celtic scale. Then the HDharmonica scale and mode is the 3rd mode of the Celtic 6-notes scale, while the one that I used in my previous post is the 5th mode of the Celtic 6-notes scale. Well.....at this point the idea of Brendan and my idea coinside from different origins and goals. I am ..glad. Actually Brendan's instict was Brilliant as this Hexatonic scale is maximal harmonic in the sense that among the 6-notes scales it has a maximum number of standard chords like major , minor etc, thus it will definetly sound of better harmony than other 6-notes scales. His choice of the mode of EDharmonica is also best for Blues. I chose a different mode of it based on my tastes. Brendan definetely deserves a pattent, for this as an harmonica. On the other hand the sequence 2-3-2-2-2-1 (e.g. C-D-F-G-A-B) IS NOT A CYCLIC PERMUTATION of the 2-2-3-2-2-1 or 1-2-2-3-2-2 or 3-2-2-1-2-2 and it should be considered a different scale than the Celtic 6-notes (minor) not a different mode of it. It could be called maybe Celtic 6-notes major, because both the Blow-row chord and the draw-row chord are major chords. MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW. Below is the table of such a tuning for a harmonica starting from D, and not C but with the same interval structure 2-3-2-2-2-1. And there is alo the inverse of this scale with interval structure 2-1-2-2-2-3 E.g. again derivable from the 7-notes C major mode of the diatonic scale , but now we omit C. Thus D-E-F-G-A-B-D . I believe the previous discussion completely clarifies the distiction between a scale and its modes.
The Byzantine culture absorbed the musical culture of Ancient Greece, that used mainly not 7-notes scales but 4 and 5 notes scales of total length an interval of 4th or 5th (called tetrachorda). The names of the modes Ionian, Dorian, Phrygian , Lydian etc were originally different 7-notes scales in the Byzantine empire relevant to the places in Greece that were mostly used, that when the European culture after Bach absorbed them in the 12-notes equal tempered system, thet altered them, and they ended to become different modes of the one diatonic scale and not different scales.
Hexatonic scales as the one below at various modes of them are used not only at modern handpans but also at chinese Bahu flutes.
Attachments
Celtic_major.gif
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Re: THE OPTIMAL TUNING FOR ALL TYPES OF MUSIC? THE ADVANTAGES OF THE IONIAN MODE CIRCULAR TUNING

Post by drkcostas » Mon Jan 27, 2020 5:39 pm

CHROMATIC GENDRE: BLUES - COUNTRY 6-NOTES MAJOR SCALE AND THE 7-NOTES BYZANTINE PARACHROMATIC SCALE.

In ancient Greece according to Aristoxenos, there were 3 musical gendres , the diatonic , the chromatic and enharmonic which were also tetrachords (total length an interval of 4th) and pentachords (total legth an interval of 5th and consisting from an initial or final tone and a tetrachord as before) and by combing a tetrachord with a pentachord they got various 7-notes scales inside an octave . In other words the 7-notes scale was of the form Tetrachord1+2+tetrachord2 , in which case it was called two "divorced" tercahords or Tetrachord1+tetrachord2+2 or 2+Tetrachord1+tetrachord2 in which case it was called two adjoint tetrachords. 1) the Diatonic was balanced feelings (that eventually after more than 1 thousand years resulted to the 7-notes diatonic scale, and a simplified rounding of their tetrcahords to a single one was the 2-2-1 and most probably all permutations of it ) the 2) Chromatic was sad feelings (that eventually after more than 1 thousand years resulted to the 7-notes harmonic minor and double harmonic minor scales, blues scale etc , And a simplified rounding of their tetrachords to a single one was the 3-1-1 nd most probably all permutations of it ) and 3) the enharmonic was happy feelings ((all possible major 3rd intervals were usually more than all possible minor 3rd intervals and a simplified rounding to a single one was the 4-(1/2)-(1/2)) and most probably all permutations of it ) and has many similarities with the Japanese 5-notes scales like the Akebono with interval structure 4 - 2 - 1 - 4 - 1 e.g. at the mode 2-1-4-1-4 e.g. A B C E F A. (See e.g. the video https://www.youtube.com/watch?v=vv7CO-nVFj8 )
According to the wikipedia (https://en.wikipedia.org/wiki/Blues_scale), a 6-notes version of the major country-blues scale is e.g. the
C, D, D♯/E♭, E, G, A, with interval structure 2-1-1-3-2-3. Or if we prefer a root at D, then D-E-F-F#-A-B-D. Below is the table for a harmonica with such a tuning.
On the other hand historically the Byzantine empire was utilizing many 7-notes scales, not possible to include in the Bach equal tempered 12-notes chromatic scale. But 3 chromatic sacles of them are possible more or less to include, Two of the chromatic such scales are the harmonic minor (e.g. from the A natural minor we derive the harmonic minor by giving a sharp at G, thus A B C D E F G# A , with interval structure 2-1-2-2-1-3-1) and the double harmonic minor (an additional sharp to d thus A B C D# E F G# A , with interval structure 2-1-3-1-1-3-1). They where used mainly in religious hymns in the Churchs. But the 3rd such chromatic scale was used mainly in the Emperors palace and other cosmic events and was called parachromatic (see e.g. http://www.huygens-fokker.org/docs/modename.html http://www.huygens-fokker.org/scala/ ). The Byzantine parachromatic scale is called also inverse Persian or Purvi Theta scale. The part 2-1-1-3 is also known as samba pentachord in arabian culture, while the part 1-1-3 is known since ancient Greece time as the tonal tetrachord of the chromatic family. The interval structure of the parachromatic Byzantine scale is 2-1-1-3-1-1-3 . Thus starting from D , it would be D, E, F, Gb ,A, Bb, B , D We may observe that it is a 7-notes version of the Blues scale, and a tuning table for a harmonicas at the D4- major 6-notes Blues-country scale and a D4- parachromatic 7-notes scales are given below. (see also article https://simplerguitarlearning.blogspot. ... rtone.html )MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE TWO-CHORD HEXATONIC TUNING HARMONICA.
Attachments
Country_major_D4.gif
Country_major_D4.gif (19.88 KiB) Viewed 8483 times
Byzantine_parachromatic.gif
Byzantine_parachromatic.gif (21.46 KiB) Viewed 8483 times
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Re: THE OPTIMAL TUNING FOR ALL TYPES OF MUSIC? THE ADVANTAGES OF THE IONIAN MODE CIRCULAR TUNING

Post by drkcostas » Mon Jan 27, 2020 8:50 pm

CHROMATIC GENDRE: MORE 6-NOTES SCALES THAT ARE BEAUTIFUL FOR HARMONICAS. COMBINING PARTS OF THE PENTATONIC WITH CHROMATIC PARTS.

We noticed in the previous post that the Blues-country scale with interval structure 2-1-1-3-2-3, (and any cyclic permutation of it, is still the same scale although a different mode of it) sounds partially as the pentatonic scale 2-2-3-2-3 and partially with chromatic part 1-1-3 which was identified as the ancient Greek tonal tetrachord of the chromatic family. By writting the Blues scale in a different 5th mode of it (cyclic permutation) makes it more clear: 2-3-2-1-1-3 . The 2-3-2 part is inherited from the pentatonic scale 2-2-3-2-3 and the 1-1-3 is the ancient Greel tonal tetrachord of the chromatic family (that exist also in the Byzantine emperor parachromatic 7-notes scale). Such scales may be obviously be used in Gypsy jazz, but in ordinary western jazz too.

Other parts of the pentatonic sacle are also the 2-2-3,

1) Thus we may discover the next hexatonic scale that should sound similarly 2-2-3-1-1-3 and it is not a different mode of the Blues-country scale. In the tables below we show this tuning , when starting from the root D . Thus D-E-F#-A-Bb-B-D. It is still a 6-notes version of the Byzantine parachromatic scale of the previous post but different from the Blues-country scale, still sounding in a similar way.

2) There are the invesres of course of the previous hexatonic scales a) the inverse ofthe Blues-country in the mode 2-3-2-1-1-3, which is the 2-3-2-3-1-1 (after inverting and taking a cyclic permutation of it). b) The inverse of the 2-2-3-1-1-3, which is the 3-2-2-1-1-3 ((after inverting and taking a cyclic permutation of it). We write them always so as to separate the pentatonic part, and the chromatic part.

3) If we combine now the pentatonic part 2-3-2 (of the Blues scale) with the chromatic part 1-3-1 (which exists in the harmonic minor) we get a hexatonic scale 2-3-2-1-3-1, that sounds partially as pentatonic and partially as chromatic (harmonic minor). It is a 6-notes version of the harmonic minor scale,perfect for harmonicas that favor in the cyclic tuningthe hexatonic scales. Some times it is also called the Erik Satie hexatonic scale . (See e.g. the video https://www.youtube.com/watch?v=okU96j6ThIM&t=8s ) We give below the tuning table when starting from the root D. And of course there is the inverse of it again which is not a different mode of it. D-E-G-A-Bb-C#-D.

4) If we combine now the pentatonic scale part 3-2-2 with the chromatic part 1-3-1 (which exists in the harmonic minor) we get a hexatonic scale
3-2-2-1-3-1, or at a different mode as 2-1-3-1-3-2 that sounds partially as pentatonic and partially as chromatic (harmonic minor). It is a 6-notes version of the Neapolitan scale 2-1-3-1-1-2-2 (e.g. from D it would be D-E-F-G#-A-Bb-C-D), perfect for harmonicas that favor in the cyclic tuning the hexatonic scales. We give below the tuning table when starting from the roor D thus D-E-F-G#-A-C-D , with interval structure at the mode 2-1-3-1-3-2 .And of course there is the inverse of it again which is not a different mode of it.

5) If we start with the double harmonic minor, e.g. from A, it is A-B-C-D#-E-F-G#-A which has interval structure 2-1-3-1-1-3-1 , we may derive an appropriate hexatonic which contains a part ofthe pentatonic scale ,which here is the 3-2-3. The resulting scale is the 3-2-3-1-2-1, or in a different mode the 2-1-3-2-3-1. Starting from the root D it is D-E-F-G#-Bb-C#-D. The mode 1-2-1-3-2-3 would give at the Blow row a single minor chord and at the Drow row again a single minor chord.

6) There still another Hexatonic version of the harmonic minor scale which belongs to the enharmonic gendre of the next posts. the 2-1-2-2-4-1
E.g. Blow=6m=G Bb D Draw=5#dim=A C F# , in total G A Bb C D F# , whci is a Hexatonic version of the harmonic G-minor.

There are also similar hexatonic scales that are symmetric like 3-2-1-3-2-1 or 3-1-2-3-1-2 or 1-2-3-1-2-3. The latter when placed to an harmonica tuning it gives at the blow row a single chord and at the draw row again a single chord as most of the examples of hexatonic tuning here E.g. A-Bb-C-D#-E-F#-A.
MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE TWO-CHORD HEXATONIC TUNING HARMONICA.
Attachments
Alternative_blues_D4.gif
ALTERNATIVE BLUES
Alternative_blues_D4.gif (20.98 KiB) Viewed 8478 times
Hexatonic_harmonic_minor_D4.gif
HEXATONIC HARMONIC MINOR OR ERIK SATIE
Hexatonic_harmonic_minor_D4.gif (20.42 KiB) Viewed 8478 times
Hexatonic_Neapolitan_minor_D4.gif
HEXATONIC NEAPOLITAN
Hexatonic_Neapolitan_minor_D4.gif (19.78 KiB) Viewed 8478 times
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Re: THE OPTIMAL TUNING FOR ALL TYPES OF MUSIC? THE ADVANTAGES OF THE IONIAN MODE CIRCULAR TUNING

Post by drkcostas » Tue Jan 28, 2020 9:29 am

ENHARMONIC GENDRE : MORE HEXATONIC SCALES FOR HARMONICAS . UTILISING AKEBONO 5-NOTES SCALE

In ancient Greece according to Aristoxenos, there were 3 musical gendres , the diatonic , the chromatic and enharmonic which were also tetrachords (total length an interval of 4th) and pentachords (total legth an interval of 5th and consisting from an initial or final tone and a tetrachord as before) and by combing a tetrachord with a pentachord they got various 7-notes scales inside an octave . In other words the 7-notes scale was of the form Tetrachord1+2+tetrachord2 , in which case it was called two "divorced" tercahords or Tetrachord1+tetrachord2+2 or 2+Tetrachord1+tetrachord2 in which case it was called two adjoint tetrachords. 1) the Diatonic was balanced feelings (that eventually after more than 1 thousand years resulted to the 7-notes diatonic scale, and a simplified rounding of their tetrcahords to a single one was the 2-2-1 and most probably all permutations of it ) the 2) Chromatic was sad feelings (that eventually after more than 1 thousand years resulted to the 7-notes harmonic minor and double harmonic minor scales, blues scale etc , And a simplified rounding of their tetrachords to a single one was the 3-1-1 nd most probably all permutations of it ) and 3) the enharmonic was happy feelings ((all possible major 3rd intervals were usually more than all possible minor 3rd intervals and a simplified rounding to a single one was the 4-(1/2)-(1/2)) and most probably all permutations of it ) and has many similarities with the Japanese 5-notes scales like the Akebono with interval structure 4 - 2 - 1 - 4 - 1 e.g. at the mode 2-1-4-1-4 e.g. A B C E F A. (See e.g. the video https://www.youtube.com/watch?v=vv7CO-nVFj8 ). One natural way to derive a hexatonic scale is to require that part ofthe hexatonic scale is either in the pentatonic or in the 7-notes diatonic. Thus here the two versions 2-2-2-1-4-1 and 2-2-2-4-1-1 may be obtained. In notes relevant to the D major scale at appropriate modes are 1) 4-1-2-2-2-1 as D-F#-G-A-B-C#-D and 2) 1-2-2-2-4-1 as A-B-C#-F-F#-G-A
Below are tables of tuning for such harmonicas. The first version is often found in Cretan improvisational dancing music (mantinades)
Still one more hexatonic with rather familiar sound is the 2-2-1-2-4-1, which can be obtained my omiting a note from the 7-notes diatonic scale E.g. C D E F G B C. For the D major scale it would be D E F# G A C# D. Its tuning table is shown below when starting from C3. It is an harmonica not to play all possible songs in it (such would be a cyclic tuning one) but to play melodies that are easily accompanied by two only chords the I=1Major, and viidim=7diminished (which sounds like the V7) as all the blow row is the 1major and all the draw row is the 7diminshed.
THIS CASE OF 2-2-1-2-4-1 IS OF EXTREME IMPORTANCE AS IT PRODUCES HAPPY MUSIC much happier than blues with the Richter tuning with a universally standard pair of chords 1major, 7diminihed. E.G. FOR C MAJOR IT IS C MAJOR-Bdiminished AND IN NOTES C-D-E-F-G-B-C AS IN THE TABLE BELOW.

And there is also the very beatiful 2-2-1-4-2-1 that when tuned at an harmonic gives the Blow-row a minor chord and the draw-row a dimished chord.
Similarly the 2-2-1-2-1-4 or D E F# G A Bb D which can be considered a hexatonic version of the G melodic minor.

Other beatiful such scales that combine the Chromatic with the enharmonic gendre are the 2-1-4-1-3-1. The Blow-row is a major chord and the draw-row another major chord one semitone apart. We could call it Hexatonic enharmonic harmonic minor.
More such scales are the 4-3-1-2-1-1 and 4-3-1-1-2-1 that start with a major chord (4-3) and the 3-4-1-1-2-1 and 3-4-1-2-1-1 that start with a minor chord.
More examples are symmetric hexatonic scales like the 1-1-4-1-1-4, or non-cyclic permutations of them like 4-1-4-1-1-1, and 4-4-1-1-1-1.
Some of these hexatonic scales have been used in handpans, mainly with indish culture names. Some of them I have classified (with no names) in the article https://simplerguitarlearning.blogspot. ... -that.html I remind the reader that in this duscussion a hexatonic scale is a sequence of 6 numbers that denote semitones, that give total sum 12, and all cyclic permutations of it, that give its 6 modes. Some such scales are self-inverse some not.
MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.
ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE TWO-CHORD HEXATONIC TUNING HARMONICA.
I have not checked exactly some similar ideas of Brendan Power for Chinese or Japanese-like tunings of the harmonica, but maybe some tunings might coincide.
Attachments
HEXATONIC_ENHARMONIC_HARMONIC_MINOR_G3.gif
Hexatonic enharmonic harmonic minor G3
HEXATONIC_ENHARMONIC_HARMONIC_MINOR_G3.gif (21.7 KiB) Viewed 8375 times
Heaxtonic_akebono3_1M_7dim_C3.gif
HEXATONIC AKEBONO3
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Heaxtonic_akebono.gif
HEXATONIC AKEBONO
Heaxtonic_akebono.gif (21.37 KiB) Viewed 8434 times

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