Re: [tuning] Digest Number 3779

hi Petr!
i have quite few recordings of Hardinger fiddle music , mainly played by Hauk Buen and have noticed the predominant microtonal intervals, especially in the upper octave .
Do you know if and if and or where there has been any measurements made of what actually is played.
It is hard to consider this stuff as just 'folk' music since it is so highly developed compositionally

>
>Message: 3 > Date: Mon, 21 Nov 2005 13:39:35 +0100
> From: Petr Pa��zek <p.parizek@chello.cz>
>Subject: Groven's tuning - another reason why 36 tones
>
>Hi.
>
>I've just read Monz's article on Groven's organ tuning. I'm glad to see this
>on your website, Monz. When you are discussing why Groven chose 36 tones for
>his tuning, I'd like to add one more. Somewhere else on the web, I found
>another paper emphasizing Groven's fondness of Norwegian folk music which
>sometimes uses intervals as 11/8 or 13/8. He also wanted to be able to
>"imitate" this in some way. He was aware that stacking 30
>1/8-schisma-tempered fifths downwards makes an interval which is about 3
>cents away from 11/8 (not counting the octave inversions, of course) and
>that stacking 33 fifths downwards makes an interval which is about 3 cents
>away from 13/8. So it was a good decision for him to choose 36 tones as the
>interval of 35 fifths made it possible to approximate 13/9 very well. I'm
>just wondering why he also had a 43-tone version of this. So far I haven't
>found any new advantages if this other than the possibility of
>transposition. What I'd prefer is a 48-tone version (what a coincidence,
>another multiple of 12?) which makes it possible to "imitate" one 7-limit
>chord very closely as the interval of 7-5 can be approximated well by
>stacking 47 fifths. In this case, I prefer to use 1/9-schisma tempering
>instead of 1/8-schisma.
>
>The complete tuning follows. Sorry for not substituting the cent sizes of
>the JI intervals by their respective ratios. I've just made the scale and
>this is what has come out.
>
>
>
>! 48temp.scl
>!
>48-tone chain of 1/9-schisma tempered fifths
> 48
>!
> 20.85505
> 41.71010
> 70.45535
> 91.31040
> 112.16545
> 133.02049
> 161.76574
> 182.62079
> 203.47584
> 224.33089
> 273.93119
> 294.78624
> 315.64129
> 336.49634
> 365.24158
> 386.09663
> 406.95168
> 427.80673
> 477.40703
> 498.26208
> 519.11713
> 539.97218
> 568.71743
> 589.57248
> 610.42752
> 631.28257
> 660.02782
> 680.88287
> 701.73792
> 722.59297
> 772.19327
> 793.04832
> 813.90337
> 834.75842
> 863.50366
> 884.35871
> 905.21376
> 926.06881
> 975.66911
> 996.52416
> 1017.37921
> 1038.23426
> 1066.97951
> 1087.83455
> 1108.68960
> 1129.54465
> 1179.14495
> 2/1
>
>
>Petr
>
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 4 > Date: Mon, 21 Nov 2005 15:30:11 +0200
> From: <oyarman@ozanyarman.com>
>Subject: Re: Re: Boethius modal system, chapter 15 of Book 4
>
>Dear Monz,
>
>
>----- Original Message -----
>From: "monz" <monz@tonalsoft.com>
>To: <tuning@yahoogroups.com>
>Sent: 18 Kas�m 2005 Cuma 11:33
>Subject: [tuning] Re: Boethius modal system, chapter 15 of Book 4
>
>
> >
>>Hi Ozan,
>>
>>
>> >>
>
>What happened to Oz? I liked it better.
>
>
> >
>>>I have prepared two colored version which I uploaded at
>>>http://www.ozanyarman.com/anonymous/
>>> >>>
>>
>>Those are awesome!
>>
>> >>
>
>
>Thanx.
>
>
> >
>>But ... what do the different colors represent?
>>
>> >>
>
>
>Green=pitches employed just once, regardless of octave equivalance.
>Yellow & Red=pitches used more than once.
>
>I used the latter in such a way that adjacent pitches from low to high
>seperated by a semitone are colored seperately & consecutively for easier
>reading.
>
>Here is another table (tones differing by a comma are marked with "o"):
>
>
>.............HD....HP....HL....D.......P.....L.....M.....H
>G...........x............................................................
>A...........x.........x..................................................
>Bb.........x.............................................................
>B......................x.......x.........................................
>C...........x.........x................x.................................
>C#............................x..........................................
>D...........x.........x.......o.......x.......x........................
>Eb.........x...........................x.................................
>E......................x.......x................x......x.................
>F............x........o................x.......o.............o.........
>F#.............................x........................x................
>g............x.........x.......o.......x.......x......o......x......x
>ab..........x...........................x......................o........
>a............x.........x.......x................x.......x..............x
>bb..........xo.......x................o......x..............o......x
>b.......................x.......x........................x...............
>c.............x........ox.....o........x......x......o......x......x
>db/c#.........................x........x.....................x.........
>d.............x.........x......ox......x.......x......x..............x
>eb...........x..........................xo......x............o.......x
>e........................x.......x................x......x...............
>f..............x.........o................x......ox.....o.....x......x
>f#/gb..........................x........................x......x........
>g'............x.........x.......o.......x........x.....ox....x......x
>a'b.......................................x......................xo....x
>a'.......................x.......x.................x......x.............x
>b'b.......................................x.......o.............x.....ox
>b'................................x.........................x.............
>c'..........................................x.......x......o......x.....x
>d'b................................................................x.....
>d'..................................................x.......x.............x
>e'b................................................................x.....x
>e............................................................x.............
>f'....................................................................x....x
>g'.........................................................................x
>
>
>
> >
>>Also, i'll post my analysis of the various cents-values
>>when the Didymus tuning is used ... can you make a
>>version which uses 19 different colors to code the
>>different pitch-classes in that tuning?
>>
>>
>> >>
>
>
>Certainly, once I see the tuning you analyze.
>
>
> >
>>And in the version which uses modern octave-equivalent
>>Roman-letter notation, why did you choose to base the
>>system on "G" rather than on "C"? It's clear that the
>>Lydian mode was the reference mode, whose mese should
>>be called "A", which bases the whole system on "C".
>>
>>
>> >>
>
>
>But then, the tonics of transpositions of the modes do not equate to the
>natural tones of the diatonic scale we recognize today, which are G A B C D
>E F G from Hypodorius to Hypermixolidius in Boethius's diagram. However, it
>is possible to transpose all the tones a pure fourth up - to the detriment
>of Mixolydius which would then start on Bb - if we were to remain true to
>the letters.
>
>
> >
>>>>In chapter 17 Boethius gives a *painstakingly detailed*
>>>>description of that diagram, indicating precisely how
>>>>notes in boxes right next to each other indicates that
>>>>there is a semitone between them, but that an empty box
>>>>between two notes indicates a whole-tone between them.
>>>>
>>>> >>>>
>>>I would urge you once more to bring forth the translations
>>>of the following chapters.
>>> >>>
>>Ozan, i've now neglected almost an entire week of important
>>work that i have to do, because i got caught up in this,
>>and i can afford to neglect it no longer. Some of this stuff
>>will just have to wait.
>>
>>
>> >>
>
>
>I understand. I am grateful for the time you spared.
>
>
> >
>>>Not so fast my colleague... I am still trying to understand
>>>why there is so much contraversy between chapter XV and
>>>consequent chapters of the 4th volume of De Institutione
>>>Musica.
>>> >>>
>>I believe i've pinpointed it: Boethius gives a detailed
>>description of species, as his introduction to a discussion
>>of the modal system ... then promptly ignores it when
>>he gives the actual description of the modal system!
>>
>> >>
>
>
>A bit crude.
>
>
> >
>>After explaining clearly and in detail the concept of
>>modal rotation thru species, he then gives an elaborate
>>diagram which presents the modal system as transpositional
>>rather than rotational.
>>
>>
>> >>
>
>
>
>So he uses mode very much out of context here to the point of contradicting
>his previous - more original and valid? -statements. I wish to know what you
>think of my categorization of terms so far:
>
>1. Modes are rotations of a single diatonical scale, so that the tonic is
>shifted over to the other available `natural` degrees of that scale .
>
>2. A specie of the octave (hence trope) is a rearrangement of notes in a
>fixed octave tuning so that the distribution of small and large intervals
>yield different `transposed modes`.
>
>3. Genera are rather reserved for tetrachords, but in principle are no more
>different compared to the construction of species.
>
>4. Boethius's diagram represents transpositions of the Lydian mode over the
>tonics of the other modes.
>
>5. Tone should be reserved for describing the relationships between modes,
>sometimes synonymous with the tonic, a derivative function of KEY.
>
>
> >
>>>That is good news. But perhaps you would like to
>>>include my interpretation also?
>>> >>>
>>Yes, sure ... but as i did more and more research into
>>the Greek modal system, i stopped working on my paper
>>on Boethius when i became unsure if my interpretation
>>was really correct. As i've said, there are many divergent
>>opinions on the rotation-vs.-transposition issue, among
>>the various scholars of ancient Greek music-theory.
>>
>>I finally got so thoroughly confused that i just gave up.
>>But at least now i've convinced myself that my
>>transpositional interpretation of that chapter 16
>>diagram is correct.
>>
>>
>>In fact, i just came across some other notes, and
>>there's a sheet of music-paper dated 2004.08.01 on
>>which i wrote out the entire modal system with the
>>Greek symbols above the notes, which is again exactly
>>the same as the interpretation given in my 1996 and
>>in the diagram i posted yesterday -- i.e., *that* was
>>the second time i independently arrived at this conclusion,
>>and yesterday's was the *third* time i did it!
>>
>>And at the bottom of this sheet of music-paper, i wrote:
>>
>> >>
>>>>" -- exactly the same as what i derived for
>>>>Aristides Q. [Quintilianus] (book 1, ch. 11) in 1998 !!
>>>>see Barker 1989, p. 420 ff."
>>>> >>>>
>>So there's a *fourth* interpretation i derived of the
>>Greek notation of the modal system, this time for
>>Aristides, which again coincides with this one.
>>
>> >>
>
>
>
>Seeing as mode is used both to describe octave species and transpositions,
>my estimations would then lead me to suggest that a very complex pattern of
>modulation and transposition was already in existence in early Medieval
>theory and possibly even before.
>
>
> >
>>So anyway, i'll have to finish the paper on Boethius
>>first, before i can include anything by you -- and
>>that is simply not going to happen until after February.
>>Too many other committments before then.
>>
>>
>> >>
>
>
>Acknowledged.
>
>
> >
>>>>What *is* an interesting topic for further research is
>>>>to trace how the transpositional form diagrammed by
>>>>Boethius, was somehow transformed into the rotational
>>>>species form which took root during the Frankish era.
>>>>
>>>> >>>>
>
>
>
>Not transformed, perhaps... but simplified to the detriment of available
>transpositions?
>
>
>
> >
>>>That is the crux of the issue! Maybe Boethius used the
>>>same terminology to indicate two very different things:
>>>octave species and transpositions of a single mode?
>>>Perhaps he attempted to demonstrate how to change
>>>pitch-levels for singers?
>>> >>>
>>Quite possible. I hope i've provided enough material
>>here to get other folks interested enough to do some
>>digging of their own.
>>
>> >>
>
>
>It has been a most productive session for me.
>
>
> >
>>>>Actually, a history of the modal system should start
>>>>with Aristoxenus, as he was the first theorist to write
>>>>about it.
>>>> >>>>
>>>Sounds like a worthwhile endeavour. You are of course
>>>the expert on this issue and all I can do is introduce
>>>a new outlook on existing materials.
>>> >>>
>>I wish that someone else would be interested enough
>>to take on the job of editing my Aristoxenus webpage
>>into something readable.
>>
>>http://tonalsoft.com/monzo/aristoxenus/318tet.htm
>>
>>I've only managed to make about the first 1/5 of it,
>>and the very last section ("Amendment from 2003.07.20"),
>>look decent.
>>
>> >>
>
>
>If only I could, but I have little knowledge on Aristoxenus to aid you in
>that direction.
>
>
> >
>>
>> >>
>>>>Anyway, no ... remember? -- Hucbald's achievement was
>>>>the *gestalt shift*. He explained the old Greek system,
>>>>with its ascending s-t-t tetrachordal interval pattern,
>>>>then explained how the "modern" modes should be fit into
>>>>the system with the t-s-t pattern, *using the same
>>>>Greek note names*. So the low G is proslambanomenos.
>>>> >>>>
>>>So you say.
>>> >>>
>>It's not *me* saying it, it's Hucbald!
>>
>>http://www.music.indiana.edu/tml/9th-11th/HUCHAR_TEXT.html
>>
>>
>>There is an English translation of Hucbald available,
>>and i have it. When i get the time, i'll post the
>>relevant excerpts.
>>
>> >>
>
>
>
>I'll take your word for it till then.
>
>
>
>
> >
>>It's out-of-print now, so your best bet is a good library:
>>
>>http://www.worldcatlibraries.org/wcpa/top3mset/aabe08529f14f206.html
>>
>>I tried searching Turkey and all of the nearby countries
>>with no luck ... the closest i've found to you which has
>>it is here:
>>
>>Accademia Della Crusca Villa Medical Di Cast, Firenze, Italy
>>
>>
>> >>
>
>
>
>Thank you so much!
>
>
> >
>>-monz
>>http://tonalsoft.com
>>Tonescape microtonal music software
>>
>>
>>
>>
>>
>> >>
>
>
>Cordially,
>Ozan
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 5 > Date: Mon, 21 Nov 2005 15:49:59 +0200
> From: <oyarman@ozanyarman.com>
>Subject: Re: Re: Boethius modal system, chapter 3 of Book 4
>
>Hi again Monz,
>
>
>----- Original Message -----
>From: "monz" <monz@tonalsoft.com>
>To: <tuning@yahoogroups.com>
>Sent: 18 Kas�m 2005 Cuma 12:11
>Subject: [tuning] Re: Boethius modal system, chapter 3 of Book 4
>
>
> >
>>Hi Ozan,
>>
>>
>> >>
>
>SNIP
>
> >
>>I've just come across a pertinent statment by Boethius
>>in his book 4, chapter 3:
>>
>>
>> >>
>>>>[-f.70r-]
>>>>Musicarum per grecas ac latinas litteras notarum nuncupat.
>>>>The naming of musical notes in Greek and Latin scholarship
>>>>
>>>><snip>
>>>>
>>>>
>>>>Sed iis omnibus modis. unum interim lidium. eiusque
>>>>notulas per tria genera disponamus. in reliquis modis
>>>>idem facere in tempus aliud differentes.
>>>>
>>>>For the present, let us take just one of the modes,
>>>>the Lydian, and arragne its written symbols thru the
>>>>3 genera; we defer doing the same with the other modes
>>>>until another time.
>>>> >>>>
>>Again demonstrating that the Lydian mode was the
>>"reference mode" for Boethius.
>>
>> >>
>
>
>Which agrees with my propositions thus far.
>
>
> >
>>>>Sane si quando dispositionem notarum grecarum litterarum
>>>>nuncupatione descripsero: lector nulla nouitate turbetur.
>>>>
>>>>Surely if i sketch the disposition of notes using the
>>>>names of Greek letters, the reader should not be put off
>>>>by anything unusual,
>>>>
>>>>
>>>>Grecis enim litteris in quamlibet partem nunc imminutis.
>>>>nunc etiam inflexis. tota [uel rata supra lin.] haec
>>>>notarum descriptio constituta est.
>>>>
>>>>for this whole arrangement of notes has been organized
>>>>around Greek letters, which are sometimes altered and
>>>>sometimes even rotated thru various positions
>>>> >>>>
>> >>
>
>
>Aha. Rotated is the word.
>
>
> >
>>[i.e.: The basic symbols for the moveable notes were for
>>the diatonic genus, and they were rotated in one direction
>>for the chromatic genus, and in the other direction for the
>>enharmonic.]
>>
>> >>
>
>
>modulations of the diatonic genus of the tetrachord?
>
>
> >
>>>>Nos uero cauemus aliquid ab antiquitatis auctoritate
>>>>transuertere.
>>>>
>>>>We, of course, guard against changing anything
>>>>handed down by the authority of antiquity.
>>>> >>>>
>> >>
>
>
>Meaning: `we are conservative when it comes to the lettering of the
>pitches.`
>
>
> >
>>With regard to the possibility of corruption of the text
>>by the medieval scribes, i draw your attention to that
>>last sentence by Boethius.
>>
>> >>
>
>
>I am hyper-attentive.
>
>
> >
>>Thus, if scribes would be especially careful about
>>*anything* in this book, it would be Boethius's handling
>>of the Greek-letter musical notation, despite the fact
>>that they didn't know how to read Greek (which is an
>>argument for the ease with which it could be corrupted).
>>
>>
>> >>
>
>
>The letters themselves are not as much important as their arrangement in the
>table coupled with his previous statements on tropes and modes.
>
>
> >
>>-monz
>>http://tonalsoft.com
>>Tonescape microtonal music software
>>
>>
>>
>>
>> >>
>
>
>Cordially,
>Ozan
>
>
>
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--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
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