A Tampered Tuning – Proposition For A Novel (?) Tempered Scale. Berlin, 19.08.2021 by gm aka Ainegil Aenor We propose a novel (?) tempered tuning in the tradition of Valotti and Young. Since the theory of circular tunings is well established and beyond the scope of this brief we skip straight to a simplistic modern day layman algorithmic construction rule: Find the pitches of a circular series of exact 1.5 frequency ratio fifths, and the corresponding diversion from 12TET. Match thirds as closely as possible. For this we need to correct each successive pitch by the value of the schism per step. Since a series of 11 of such steps will end up on a higher pitch than the starting note, we look for a continuous pattern of steps that either go up or down by the corresponding value of the schism. The deviation of Youngs classic solution from 12TET for this is shown in Fig. 1. A novel proposed solution is depicted in Fig. 2. The deviation of a natural just scale from 12TET is shown in Fig. 3. The resulting frequency ratios, relative pitches and pitch deviations are given in Table 1. Our solution differs from Youngs solution mostly by the asymmetrie and a slightly closer resemblance to the just scale in terms of tendencies. In comparison to 12TET our scale has more exact fifths and a closer major third, as expected. The motivation for this was personal interest in a personalized and novel tempered scale. It is unknown to the author whether this scheme or scale was already known. No references for this could be found. It is now left to the reader to evaluate the proposition in theoretical and musical terms. References: 1. Constructing an Optimal Circulating Temperament based on a Set of Musical Requirements Ivar Farup Gjvik University College, P.O.Box 191, N2802 Gjvik, Norway (submitted July 2013) 2. https://www.math.uwaterloo.ca/~mrubinst/tuning/tuning.html Figure 1: Youngs Scheme Figure 2: The proposed detuning and construction scheme Figure 3: Just Frequencies deviation from 12TET Table 1: The Proposed Scale Frequency Ratios Pitch Cents Deviation from 12TET 1 0 0 1.05825 98.0102 1.98975 1.11998 196.165 3.83538 1.19057 301.99 1.98975 1.25435 392.329 7.67076 1.33632 501.918 1.91769 1.41097 596.021 3.9795 1.49665 698.082 1.91769 1.5874 800 0 1.67621 894.247 5.75307 1.7859 1003.98 3.9795 1.88125 1094.03 5.96925 * the values have been calculated with reduced resolution and might contain rounding errors
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