> This message is in MIME format. Since your mail reader does not understand this format, some or all of this message may not be legible. ---------------------- multipart/mixed attachment Here are two very interesting shots. You can see from these why people kept being unhappy with the tuning system. The 14th Century Pythagorean is clearly designed to have pure fifths, so ten of the twelve fifths are zero. The price for this is that the EB fifth is 15 cents narrow (compared to the ET contraction of 2 cents). There are three varieties of thirds: four at +6.8 cents, four at +12.8 cents, and four at +21.5 cents (ET uses 13.7 cents). The 1799 Meantone is clearly designed to have the fifths and thirds match each other. For the major triads on C, G, D, A, D#, A#, and F, the fifths are at -4.3 cents and the thirds are at +4.3 cents. (This is cents, not beat rates, so I'm not sure if they beat the same ... more Excel work to come...) The price for this is that three of the thirds are stretched to over 30 cents and must be unusable, and two of the fifths are actually *expanded* to +8 cents and +11 cents respectively. || ||| || ||| || ||| || ||| || ||| || ||| || ||| || ||| jason kanter * piano tuning * piano teaching bellevue, wa * 425 562 4127 * cell 425 831 1561 orcas island * 360 376 2799 || ||| || ||| || ||| || ||| || ||| || ||| || ||| || ||| ---------------------- multipart/mixed attachment A non-text attachment was scrubbed... Name: not available Type: image/gif Size: 12597 bytes Desc: not available Url : https://www.moypiano.com/ptg/pianotech.php/attachments/59/9a/2a/67/attachment.gif ---------------------- multipart/mixed attachment A non-text attachment was scrubbed... Name: not available Type: image/gif Size: 12386 bytes Desc: not available Url : https://www.moypiano.com/ptg/pianotech.php/attachments/3d/a7/9e/5f/attachment.gif ---------------------- multipart/mixed attachment--
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