Gainable accuray in high precision-tuning was:Re: epimoric bisection 81:80
- --- In email@example.com, "Brad Lehman" <bpl@...> wrote:
simply short all nominators over denominators by the factor 10
in order to meet scala the convention of integral fractions:
SC=80:81 inbetween F~C~G~D~A~E & schisma in E~B_F#_C#_G#~Eb~Bb~F
2790/2643 ! 279.0C#4 / 264.3C4
2960/2643 ! 296.0D_4 / 264.3C4
6275/4926 ! 627.5Eb4 / 528.6C5
6615/4926 ! 661.5E_4 / 264.3C4 = (5:4)(882:881) ~+1.964 Cents sharp
3524/2643 ! 352.4F_4 / 264.3C4 = (4:3)(882:881) ~+1.964 Cents sharp
3720/2643 ! 372.0F#4 / 264.3C4
3960/2643 ! 396.0G_4 / 264.3C4 = (3:2)(880:881) ~-1.966 Cents flat
4185/2643 ! 418.5G#4 / 264.3C4
4425/2643 ! 442.5A_4 / 264.3C4 440Hz(+2.5Hz = 150 MetronomeBeats/min)
4705/2643 ! 470.5Bb4 / 264.3C4
4960/2643 ! 496.0B_4 / 264.3C4
That results in epimoric beating lowered 5ths, all amounts given
in rational, ~Cents~ & ~TUs~ for the Syntonic-comma in F~C~G~D~A~E
F 881:882 C 880:881 G 296:297 D 295:296 A 294:295 E = product 80:81
F ~-1.963 C ~-1.966 G ~-5.839 D ~-5.859 A ~-5.879 E = sum ~-21.506C
F ~-60.28 C ~-60.34 G ~-179.2 D ~-179.8 A ~-180.4 E = sum ~660.04TUs
and the schisma = 2^15/5/3^8 = 32768:32805 ~-1.954Cents ~-59.96TUs
E 3968:3969 B_F#_C#_G# 2510:2511 Eb 3764:3765 Bb 4704:4705 F
E ~-0.43624 B_F#_C#_G# ~-0.68959 Eb ~-0.45988 Bb ~-0.36799 F
E ~-13.3886 B_F#_C#_G# ~-21.1641 Eb ~-14.1141 Bb ~-11.2940 F
>The wanted precision of accessible accuracy
> With only an A=440 tuning fork in one hand, a harpsichord tuning lever
> in the other hand, and absolutely NO electronic devices of any kind:
> how exactly should one proceed to get all twelve of your notes
> correctly tuned onto a harpsichord, using this scheme?
depends on several factors:
1. Quality of tuneability for the instrument alike
deviations due to inhamonicty of the strings?
2. Counting beats barely by own heart-pulse of
under aid of an clock or even better an adjustable Metronome?
3. Tuner is rested/relaxed or fatigued/exhausted or
may be even incompetent?
> And with noIn yours personal "squiggle" impreciseness
> way of measuring integer frequencies, either, or knowing when they've
> been achieved precisely?
of barely PC^(1/12)= 60TUs
probable the following rouding would be sufficient
for yours personal taste?:
F -1 C -1 G -3 D -3 A -3 E for approximation of about an ~SC
F -60 C -60 G -180 D -180 A -180 E for exaclty 660TUs~=~SC
E -0.25 B_F#_C#_G# -0.25 Eb -0.25 Bb -0.25 F in PC^(1/12) units
E -~15~ B_F#_C#_G# -~15~ Eb -~15~ Bb -~15~ F with sum=60TUs=~schisma
>That approximation in yours personal style
> To what precision are errors acceptable? And why?
-if you would achive 15TUs = PC^(1/48) = ~0.5 Cents
would deviate maximal even less than 6 TUs = PC^(1/120) ~0.2 Cents.
>Never at all, due to the possibilty to translate into
> Does one first have
> to agree with your goal of proportional beating, and your constraint
> of integer frequencies?
your's terms within an error of less than ~1/5 Cents.
> All this stuff just looks likeNo problem.
> nearly-meaningless tables of numerals to me, sorry;
How about that "squiggle"-type notation with 4 different grades of
5ths with the cycle:
with extended legend that has additional an dot "." for PC(-1/48)
' = PC(-1/12)
''' = PC^(-1/4) as in W#3 on the average C'''G'''D'''A_E_B'''F#_..._C
. = PC^(-1/48) that 1/4 of yours usual unit '
_ = an JI 5th of exactly 3/2=1.5
If you don't accept PC^(1/48) = ~schisma^(1/4) as smallest unit
then try intead that modifiaction
without any subschismatic refinements:
> the only way II.m.h.o. ~0.2 Cents on the average in precision will suffice enough.
> know to assess its quality is to see if it agrees with *your own*
> which doesn't tell us one way or another about the usefulnessMeanwhile I'm more tolerant in that aspect:
> for anything else *but* your own goal of proportional beating (or
> whatever it is).
Never mind if you persist in inprecise tuning-methods
without counting beats exactly.
>Simply try it out!
> If I'd somehow take the time and get this temperament set up on my
> within some acceptable error tolerance but without usingSurely with yours ability and daily practice
> any electronic devices:
in hearing you should achieve at least for:
an exactness of
even less than about PC(-1/24)accuracy
or equivalent ~1 Cents precision an the average.
> how would the resulting temperament sound inWorks fine, due to the pronouced Baroque key-characteristics.
> playing (say) some late Couperin?
> What does it do for the music,C-major deviates the least from JI.
> harmonically and melodically?
> That's the kind of thing I personallyeven my modern 3-fold stringed piano with 88keys over 7 octaves
> care about: a temperament that sounds great in the music, and that
> be done entirely by ear in less than 10 minutes without having to
> calculate (or even refer to) a page of numbers.
needs only a few minutes retuning when the weather changes.
>Transposing is no problem for scala.
> And, what happens if I'd want to start on A=430 or something else
442.5 / 430 = 177/172 = 35.4/34.4 = ~1.02906977... or ~2.9 %
(1 200 * ln(430 / 442.5)) / ln(2) = -49.6089545...Cents
that's about an half of an 12-EDO semitone = 50Cents lower than 442.5.
Where's the problem there,
except that for A4=430Hz the string tension becomes to loose in an
modern standard piano?
> (maybe not having anything to do with integers!), or on some C?Scala does that job quite well.
> it all need to be recalculated?
> Help out the practical musicians whoPlease let me know your's opinion
> just want to listen to the sounds of intervallic relationships,
after you have tryed out some of the above versions.
I do agree with you, that without:
> calculatingthe corresponding acustical ratios, there is almost
>nothing....understood in tempering key-instruments in an properly way.
- Dear Mike, my apologies for the very late reply. As I have stated in
my recent message to Margo Schulter, I had been enjoying a well
deserved summer's rest.
To answer your enquiry, here are some links to older messages to this
forum on the subject of masters of Turkish maqam music:
The names of some of the prominent masters have been listed in these
messages. A search in amazon.com could yield links to the performances
of masters themselves.
Fusion type endeavours in "world music" does occasionally result in
original productions worthy of approval. However, for a crash course
in maqam music, you need to listen to acclaimed executants and
venerable exponents of the tradition, not syntheses.
Direct personal experience of Allah is very much ingrained in Sufi
music. Most of the known neyzens in Turkiye are into tasavvuf. You are
likely to enjoy the Erguner brothers, the elder of which, Kudsi, has
done world fusion too if I heard correctly:
If you are into the Turkish ney for the love of its trancendental
sound, here are acknowledged quotidian performers of the instrument:
On Jun 28, 2008, at 7:42 AM, Mike Battaglia wrote:
> On Fri, Jun 27, 2008 at 8:15 PM, Ozan Yarman <ozanyarman@...
> > wrote:
>> I think the theory of Maqam music and other "ethnic" genres around
>> world are much neglected by the alternative tuning list community.
>> Most of the discussions are centered around either historical or
>> contemporary microtonalisms for furthering Western music culture
>> alone. While I appreciate the contributions by the West to musical
>> art, I believe the Western quarter (pun intended) can account for
>> a fraction of the actual music-making in the globe. One of the
>> greatest traditions is right next door: A venerable monophonal Middle
>> Eastern culture based on maqamat, destgaha and raga. This "exotic"
>> culture has been influenced by a thousand years of Islamic atmosphere
>> to inspire such styles and practices as Mevlevi rites, Qawwali
>> performances, peshrevs, taqsims, gazels, etc... Your penchant to
>> discover more of the theories and styles of exotic traditions is
>> Though my experience is most inadequate to describe the musical
>> wonders of the Islamic Civilization, my presence in the tuning list
>> a fresh academician should be construed as an oppurtunity to discover
>> a glimpse of at least the Turkish branch of this grand culture.
> Well hey man, if you have a listening list of stuff you can recommend,
> I think we'd all love to check it out. World music is one of the most
> fascinating things in the, well, the world. Mainly because you have
> thousands of years of musical development behind most of these
> cultures and styles, and so they are usually very much advanced.
> Jeff Buckley did a Qawwali-inspired song, "Dream Brother," in which he
> mixed pop/rock with traditional Qawwali elements, and it's one of my
> favorite songs. I started looking for some traditional Qawwali
> recordings when I heard that song, and I didn't really find much.
> Any time there is an old, ancient branch of music that has reached as
> high of a level of artistic development as the one we're talking about
> here, people will be interested. I just think many don't know about it
> One interesting thing to note is that the religious music of all of
> the world sounds very, very, very similar. Perhaps not the music that
> is "associated" with various churches and such - but the music that
> monks sing, the music that is sung to draw people closer to the
> experience of God.