This is a multi-part message in MIME format. ---------------------- multipart/alternative attachment Phil, Alan, others If you tune D3 and A4 to one beat per second at A5 then you are tuning a 1 bps 6:2 twelth type. I've never read anywhere that this is thee most central to equal temperment. Perhaps this is a typo since Alan refers to D3 and A4 at A4. Beatless here is a lowest order pure twelth, or a 3:1 type twelth. Making it perfect whilst insureing a beatless 6:3 octave at D4-D3 and barely slightly narrow 6:3 octavetype at A4 - A3 will do a some very interesting things. Number one it will re-enforce the 3rd partial of D3 but uses the 12th instead of the 5th. Number two it keeps the octave types consistant with very slowly beating 5ths. Thirdly, if the resulting temperament from these anchours is carried over in the form of tuning P 12ths upwards you will automatically find a moderate stretch that matches the pianos inharmonicity very well indeed. With just a little care one can easily get the stretch to converge on a very near just 4:2:1 double octave for the entire top octave, the highest note being slightly wide of the lower two. That is to say that from C5 upwards all double octaves are for all practical purposes just with respect to their lowest order coincidents. That near justness, coupled with the just 12ths the whole way, creates a very reenforcement of any notes 3rd partial since you end up with the 4:3:2:1 all very closely aligned. The 3:1 being barely sharp of the 4:2. Personally, I find the clarity this creates in the treble to be worth a big exclamation mark. Its like you end up hiting the sweet spot on all of those top notes without any real difficutly. A good aural test for this is just to add the 5th coincident as a test note. Say you are tuning E5 Play C3 E3, C3 A3, C3 E4, and C3 E5. Since E3 and E4 are present against C3 you are testing the 4:2 octave type. At the same time you are listening to the 3:1 12th type with E5 and A3 against C3 The resulting beat rates played in sequence should sound such that the 1st interval should beat at similar rate to 3rd interval, while the 2nd interval and 4th interval should be slightly faster. The 4th interval should not beat faster then the 2nd interval... perhaps just a nats butt slower if you feel the need to squeeze the 12th just a hair. Try it... you like it. RicB Alan Bernard writes >>>>/"/Since most temperaments work well with about 1/2 beat narrow D4-A4/ /fifth and likewise with about a 1/2 beat wide D3-D4 octave, if you tuned D3 to A4 absolutely beatless (at A5) you would have two notes (in a two octave temperament) that were dead-on and accounting for inharminicity across the break in most pianos Then, tuning A3 to A4, and D4 to D3 while checking the fourths and fifths created among those four notes you'd be pretty confident you had four solidly and rather easily placed notes.Anything wrong with this? ">>>> To whit Phil Bondi replies. Nothing wrong with the strategy, but I don't tune D3 to A4 beatless at A5. I tune them at 1 beat per second at A5 because A3 to D4 and D4 to A4 are 1bps. All three of the above mentioned intervals have their common coincident partial at A5. This is the most fundamental beat rate of equal temperament. It's very easy to achieve if you reference it with your watch. ---------------------- multipart/alternative attachment An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/1a/af/f2/a1/attachment.htm ---------------------- multipart/alternative attachment--
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