Dreyblatt tuning system: Difference between revisions
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from Arnold Dreyblatt: ''Tuning Systems Explanation'', http://www.dreyblatt.net/general-information-music#/tuning-system/ | from [[Arnold Dreyblatt]]: ''Tuning Systems Explanation'', http://www.dreyblatt.net/general-information-music#/tuning-system/ | ||
The ''Dreyblatt Tuning System'' is calculated from the third, fifth, seventh, ninth and eleventh | The ''Dreyblatt Tuning System'' is calculated from the third, fifth, seventh, ninth and eleventh [[harmonic]]s and their multiples in the following pattern: | ||
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These mathematically related harmonics are heard as tonal relationships when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural harmonic series, these tones fall (unequally) in the span of one octave in the following order: | These mathematically related harmonics are heard as tonal relationships when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural harmonic series, these tones fall (unequally) in the span of one [[octave]] in the following order: | ||
1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2) | 1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2) | ||
These tones are performed in "just intonation' based on a fundamental tone of "F". | These tones are performed in "[[just intonation]]' based on a fundamental tone of "F". | ||
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[[Category:Just intonation]] | |||
[[Category:11-limit]] | |||
Latest revision as of 05:20, 9 January 2024
from Arnold Dreyblatt: Tuning Systems Explanation, http://www.dreyblatt.net/general-information-music#/tuning-system/
The Dreyblatt Tuning System is calculated from the third, fifth, seventh, ninth and eleventh harmonics and their multiples in the following pattern:
| 1 | 3 | 5 | 7 | 9 | 11 |
| 3 | 9 | 15 | 21 | 27 | 33 |
| 5 | 15 | 25 | 35 | 45 | 55 |
| 7 | 21 | 35 | 49 | 63 | 77 |
| 9 | 27 | 45 | 63 | 81 | 99 |
| 11 | 33 | 55 | 77 | 99 | 121 |
These mathematically related harmonics are heard as tonal relationships when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural harmonic series, these tones fall (unequally) in the span of one octave in the following order:
1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)
These tones are performed in "just intonation' based on a fundamental tone of "F".
| Note | Freq. | Partial | Cents |
| F | 349.2 | 1 | 0 |
| F# | 360.11 | 33 | -47 |
| G | 381.93 | 35 | -45 |
| G# | 392.85 | 9 | +4 |
| G# | 420.13 | 77 | +20 |
| A | 436.5 | 5 | -14 |
| A | 441.95 | 81 | +8 |
| A# | 458.32 | 21 | -29 |
| B | 480.15 | 11 | -49 |
| B | 491.06 | 45 | -10 |
| C | 523.8 | 3 | +2 |
| C | 534.71 | 49 | +38 |
| C# | 540.16 | 99 | -45 |
| C# | 545.62 | 25 | -28 |
| D | 589.27 | 27 | +6 |
| D | 600.18 | 55 | +37 |
| D# | 611.1 | 7 | -31 |
| E | 654.75 | 15 | -12 |
| E | 660.20 | 121 | +2 |
| F | 687.48 | 63 | -27 |