the medieval ones. it takes very little training to hear beats in fifth.
Nope. The interval of a tempered fifth is 2 to the 7/12, which equals approx. 1.498307. You will not likely notice the difference.
Bear in mind that the removal of the comma is distributed across all the scale degrees equally in our tuning, and the comma is a very small interval.
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The modern artists are playing the modern well-tempered scale. You can hear that they are, because it doesnât sound odd. Half a millennium ago it would have sounded a bit out of tune. But not of course to the artists playing at the time.
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Then I disagree. I think that up until we had an instrument that was expected to play all of the way around the circle of fifths, then they would have used the Pythagorean fifth, because it just resonates better.
Now, if you had said that the modern artists might have performed theâŚ
⌠Then thatâs what I would have expected, just because, to modern ears, thatâs what a fifth sounds like.
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Youâre quite right. I was giving the tritone, wasnât I? Nevertheless your corrected ratio (27/12 â 1.498307) is still flatter than 1.5. And you can hear the difference, especially in lower registers. You can certainly hear the difference between (say) a C major scale in the well-tempered system and one executed in Pythagorean tuning where the ratios are rational.
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in a 1000 AD we didnât have an instrument that could play the circle of fifths?! iâll book you a plane ticket to the MiM in phoenix and we can have that discussion there 
Iâm not saying that we didnât; Iâm saying that until we started with well temperament or equal temperament, instruments werenât meant to sound good all of the way around the circle of fifths; thereâd always be a âwolfâ chord that would sound wrong.
With equal tempering, none of the chords sound perfectly right the way that they do with Pythagorean tuning, but, because the âwrongnessâ is spread equally among all twelve intervals, thereâs no one chord that sounds especially wrong.
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cracks knuckles
do we want a tuning throwdown? havenât we been doing this for millenia cause those âwolfâ chords are obvious to anyone with an ear?
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I will stick with my observation. Unless you have beating to go by (and that would be a bit rare in this music, which is monophonic with an ad libitum instrumental drone and antiphon), youâll be hard pressed to hear the difference, which is going to be well within the range of vocal vibrato.
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If you mean all twelve, using Pythagorean tuning, youâd need an instrument spanning a little over seven octaves (say you started on C at 64Hz, your G would be 96Hz, your D would be 144Hz, your A 216Hz, ⌠via your F# at 729Hz (the last integer valued frequency here), then through C#, G#, D#, A#, F to another ânearly-but-not-entirely-unlike-Câ at 8303.76âŚ, noticeably not 8192). Even if you kept occasionally dividing by two, to keep your instrument reasonable, youâd end up with âCâ at 1037 Hz, or 519ishHz, or whatever.
This is why, generally, instruments played in a particular key. They would not transpose well, even to folk used to Pythagorean scales. Itâs why we have Clarinets in A, Trumpets in Bâ etc. That they are now capable of playing well in any key, in well-tempered scales, is down to engineering.
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no you donât seven octaves. octaves are exactly proportional. and transposing down or up isnât cheating.
(btw, clarinets are usually in b flat, not A, but you generally need A clarinets for making large, difficult romantic scores easier)
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right on man.
Less than 2 cents difference.
I suppose my main point would be that - if youâre going to go to the trouble of working out what this music would have sounded like when originally played, it seems peculiar to not also use the tunings of the time as well as the notations. As it is, what theyâre playing here is right between two musics. Which neither âageâ would recognise.
Which is not to say it isnât well-executed.
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Yeah - I picked an A clarinet only to contrast it with a Bâ trumpet. Or other brass instruments in Eâ. You can get trumpets in C anyway, but that would hardly be even interesting here.
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A few months ago a friend and I tried to have a conversation with Chinese traditional musicians because we were curious about the differences in their âoctavesâ as opposed to what weâre used to in the West. We did not have enough grasp of one language between us which would sufficiently express the nuances we were all trying to understand, but one thing we definitely learned was that traditional musicians (including singers) in modern China study Western tuning and score-reading as well as their own, which is utterly different, because otherwise they canât perform with other musicians around the world. Itâs kind of like how all commercial airplane pilots around the world have to use English, even for domestic flights, because there needs to be a common standard for all.
As much as we could understand, it was fascinating to learn how differently music is written there. It reminded me so much of this early European notation. Was this another thing Marco Polo brought back to Italy?
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There seems to be a slight suggestion here that modern ears wouldnât be able to distinguish older scales from our modern compromise of well-temperedness. Have you come across - for example - Wendy Carlosâ âBeauty in the Beastâ, which employs several varieties of tunings? There are many resources demonstrating alternative tunings. Itâs not at all difficult to apprehend their difference.
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I use mean tone and well-tempered tunings as a matter of course. As a rule (including equal temperament), except for fifths in remote keys in meantone tunings, the fifths in most temperaments have very small amounts of error - the largest divergences from just intonation are in the seconds and thirds.
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Is the mean-tone fifth also a 3/2er? (I could google it I suppose, but, since weâre chatting âŚ) Would you feel an urge to flatten it, to accommodate modern ears? Would âancientâ players feel the same way? Iâm not sure they could, since theyâd have no idea of 27/12 back then. In any case, would it not also depend on the instrument? For instance the open harmonics (available with a light finger touch, not an actual stopping) obtainable from stringed instruments must be sounded with a string of 2/3 the length and therefore must sound a tad sharp. Itâs unavoidable (actual mathematical non-idealised finiticity of string diameter and weight notwithstanding) since you canât execute a vibrato under such lightnesses of touch. Presumably basic wind instruments (without complex engineering) are constrained by their standing waves - which must be in exact integer ratios.
Corvus Corax, for instance.
/ducks
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