Re: [abcusers] intonation - Fomula for determining a half step in
Phil Taylor wrote: > > That's a very dissonant interval (G#) so it probably doesn't matter > which you choose. If you want to modulate to the A then G# is the third of the dominant chord and therefore important and so it does matter. Best choisse is the third of E then. You also have a choice for the C natural, which > is much less dissonant. Instead of 9:5 you could use 16:9 which > comes out much closer to the equal tempered fraction (a couple of > cents flat). Need to do some careful listening tests to see which > sounds better. On the hurdygurdy I have the advantage to intonate the lower and push the key up to the higher :-) Simon Wascher To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] intonation - Fomula for determining a half step in
John Walsh wrote: >I wrote: > >>>(...)This effectively means that they are in some kind of just tuning: >>> the ratio of the frequency of each note to the drone frequency is a >simple >>> fraction with fairly low denominator. (...) It's close to the even >tempered >>>ale for the fifth >>> and third, not so close with the second, for instance. (15-17 cents > >And Simon Wascher replied: > >I> disagree strongly! the just third is quite far from the equaltempered. >a>nd the fifth is really different too. >> > > Sorry, I was going from memory, and had the second and third >reversed. Here is the table someone posted to the UP list. (Made up, I >am sure, with a hand calculator, not a tuner on a set of real pipes.) >Anyway, the second is reasonably close and the third is not, as you say, >but the fifth on the other hand is quite close. (There's an interesting >choice for the G#: the two possibilities differ by 35 cents.) > >NoteJust Ratio (to D)Equal tempered fraction Difference in cents >---- - >D 1:1 1.00 0 >D# 16:151.0595+12 >E 9:8 1.1225+4 >Fnat6:5 1.1892+16 (!) >F# 5:4 1.2599-14 >G 4:3 1.3348-2 >G# 7:5 or 10:7 1.4142-17 or +18 >A 3:2 1.4983+2 >A# 8:5 1.5874+14 >B 5:3 1.6818-16 >Cnat9:5 1.7818+18 >C# 15:8 1.8878-12 >D 2:1 2.0 That's a very dissonant interval (G#) so it probably doesn't matter which you choose. You also have a choice for the C natural, which is much less dissonant. Instead of 9:5 you could use 16:9 which comes out much closer to the equal tempered fraction (a couple of cents flat). Need to do some careful listening tests to see which sounds better. Phil Taylor To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] intonation - Fomula for determining a half step in
I wrote: >>(...)This effectively means that they are in some kind of just tuning: >> the ratio of the frequency of each note to the drone frequency is a simple >> fraction with fairly low denominator. (...) It's close to the even tempered >>ale for the fifth >> and third, not so close with the second, for instance. (15-17 cents And Simon Wascher replied: I> disagree strongly! the just third is quite far from the equaltempered. a>nd the fifth is really different too. > Sorry, I was going from memory, and had the second and third reversed. Here is the table someone posted to the UP list. (Made up, I am sure, with a hand calculator, not a tuner on a set of real pipes.) Anyway, the second is reasonably close and the third is not, as you say, but the fifth on the other hand is quite close. (There's an interesting choice for the G#: the two possibilities differ by 35 cents.) NoteJust Ratio (to D)Equal tempered fraction Difference in cents ---- - D 1:1 1.00 0 D# 16:151.0595+12 E 9:8 1.1225+4 Fnat6:5 1.1892+16 (!) F# 5:4 1.2599-14 G 4:3 1.3348-2 G# 7:5 or 10:7 1.4142-17 or +18 A 3:2 1.4983+2 A# 8:5 1.5874+14 B 5:3 1.6818-16 Cnat9:5 1.7818+18 C# 15:8 1.8878-12 D 2:1 2.0 Cheers, John Walsh To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] intonation - Fomula for determining a half step in MgHz...
> "Phil" == Phil Taylor <[EMAIL PROTECTED]> writes: Phil> Yes and no. the expression "well-tempered" comes from the Phil> title of Bach's two volumes of preludes and fugues. (...) >>> No, I think most people these days believe that Bach's Well-tempered >>> keyboard was not equal tempered. >> >> as far as I know it was well tempered following a system developed by a >> man called werckmeister. In systems like this you chose a number of >> consecutive fifths wich are about just intonation and divide the >> divergence between 12 just intonated fifths and the octave between the >> other fifths. As I remember, this specific system also includes a >> correction for the thirds. Phil> I stand corrected. However, if the system used involved distributing Phil> the accumulated error from twelve perfect fifths among all the notes, Phil> the result will surely be an equally-tempered scale, even though it's Phil> mathematical basis is different? Not if the error isn't distributed equally among all the fifths. I play recorder with a harpsichord which is usually tuned to some kind of seventeenth or eighteenth century tuning. As is usual, the harpsichord will "transpose", by shifting the keyboard over by one string, so that if the scale were equal tempered, the instrument could play at either A440 or A415. But when it plays at A440, what it's really doing relative to the way it was tuned is playing in the key of C# (if the piece is in C). I bought my A415 recorders because the difference between playing in C and playing in C# on an instrument in one of these tunings is not at all academic or obscure; the C# sounds pretty lousy. -- Laura (mailto:[EMAIL PROTECTED] , http://www.laymusic.org/ ) (617) 661-8097 fax: (801) 365-6574 233 Broadway, Cambridge, MA 02139 To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] intonation - Fomula for determining a half step in MgHz...
Simon Wascher wrote: >To my understanding, there are two groups of tuning systems which both >are forming the basis of western music: >1) tempered intonation scales <...> >2) just intonation scales (I do not really know if this is the right >term in english the german term is "Skalen mit reiner Intonation") Yes, it's the same in English. <...> >Laura Conrad wrote: >> >> > "Phil" == Phil Taylor <[EMAIL PROTECTED]> writes: >> >> Phil> Yes and no. the expression "well-tempered" comes from the >> Phil> title of Bach's two volumes of preludes and fugues. (...) >> No, I think most people these days believe that Bach's Well-tempered >> keyboard was not equal tempered. > >as far as I know it was well tempered following a system developed by a >man called werckmeister. In systems like this you chose a number of >consecutive fifths wich are about just intonation and divide the >divergence between 12 just intonated fifths and the octave between the >other fifths. As I remember, this specific system also includes a >correction for the thirds. I stand corrected. However, if the system used involved distributing the accumulated error from twelve perfect fifths among all the notes, the result will surely be an equally-tempered scale, even though it's mathematical basis is different? Phil Taylor To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] intonation - Fomula for determining a half step in MgHz...
Hello, > John Walsh wrote: > > In fact, the even tempered scale hasn't completely taken over. The > uilleann pipes are usually tuned against the drones, and I imagine that is > also true of the highland pipes and other instruments like the vielle > which have drones. (...) To my understanding, there are two groups of tuning systems which both are forming the basis of western music: 1) tempered intonation scales Including everything from pythagorean to equal tempered. In this system some or all intervals are made gradually imperfect to open a wider range of chromatic changes more "playable" scales on a twelve key instrument (like the piano). The common idea starts at one specific point of the musical system: dealing with the difference between the octave and the accumulation of twelve fifths. The dominance of the twelve keys per octave instrument, which is in fact one of the major reasons for this kind of tonal system, has historical reasons not entirely musical. These tempered scales, in their notation system, note names, temper relations, even the twelve tone system of semi tones still refer to the other group of scale intonations the 2) just intonation scales (I do not really know if this is the right term in english the german term is "Skalen mit reiner Intonation") In this intonation the scale is assembled out of "perfect" simple ratio intervals the specific characteristic of a scale based on the relations of the used numbers. As an example two common scales of this type: the scale used by the Alphorn which just uses the harmonics of one basic note is constructed on the numbers 7 :8 :9 :10:11:12:13 b :c :d :e :f :g :a as one can see these numbers differ strongly against equal temperament. It is used today by traditional music, singers, fiddle players, not just Alphorn players! in many european regions. The scale most drone based instruments use (not just those): 24:27:30:32:36:40:45 c :d :e :f :g :a :b this proportions are based on the ratios of only three numbers, the first three indivisible numbers 2,3,5. This makes the scale more usefull for music which contains harmonies because there are less beat-notes (ger:interferenz-töne) than in the alphorn scale wich includes ratios of many numbers such as 7:11 >(...)This effectively means that they are in some kind of just tuning: > the ratio of the frequency of each note to the drone frequency is a simple > fraction with fairly low denominator. (...) It's close to the even tempered scale >for the fifth > and third, not so close with the second, for instance. (15-17 cents I disagree strongly! the just third is quite far from the equal tempered. and the fifth is really different too. > not so close with the second, for instance. In fact in those just intonation scales I know the perfect second is a very stable nearly consonant sound, seen as fifth of the fifth. Laura Conrad wrote: > > > "Phil" == Phil Taylor <[EMAIL PROTECTED]> writes: > > Phil> Yes and no. the expression "well-tempered" comes from the > Phil> title of Bach's two volumes of preludes and fugues. (...) > No, I think most people these days believe that Bach's Well-tempered > keyboard was not equal tempered. as far as I know it was well tempered following a system developed by a man called werckmeister. In systems like this you chose a number of consecutive fifths wich are about just intonation and divide the divergence between 12 just intonated fifths and the octave between the other fifths. As I remember, this specific system also includes a correction for the thirds. Simon Wascher - Vienna, Austria To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
