File:Size of intervals in C-based asymmetric 5-limit tuning.PNG
Size_of_intervals_in_C-based_asymmetric_5-limit_tuning.PNG (455 × 433 pixels, file size: 36 KB, MIME type: image/png)
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Summary
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| Description |
English: Sizes in cents of the 144 intervals in the C-based 5-limit tuning system (asymmetric scale). The selected ratios are listed below. Bold font indicates just intervals. The values were accurately computed using Microsoft Excel, then rounded to integers. The image was produced using Microsoft Excel and captured with Microsoft Snipping Tool. |
| Date | |
| Source | Own work |
| Author | Paolo.dL |
The frequency ratios selected for this 12-tone scale, and the elementary factors from which they were computed, are shown in this table:
| Asymmetric scale | ||||||
|---|---|---|---|---|---|---|
| Factor | 1/9 | 1/3 | 1 | 3 | 9 | |
| 5 | A 5/3 |
E 5/4 |
B 15/8 |
F♯ 45/32 | ||
| 1 | F 4/3 |
C 1 |
G 3/2 |
D 9/8 | ||
| 1/5 | D♭ 16/15 |
A♭ 8/5 |
E♭ 6/5 |
B♭ 9/5 | ||
Wolf intervals are operationally defined herein as intervals composed of 3, 4, 5, 7, 8, or 9 semitones (i.e. major and minor thirds or sixths, perfect fourths or fifths, and their enharmonic equivalents) the size of which deviates by more than one syntonic comma (about 21.5 cents) from the corresponding justly intonated interval. Intervals made up of 1, 2, 6, 10, or 11 semitones (e.g. major and minor seconds or sevenths, tritones, and their enharmonic equivalents) are considered to be dissonant even when they are justly tuned, thus they are not marked as wolf intervals even when they deviate from just intonation by more than one syntonic comma.
− Paolo.dL (talk) 11:08, 29 July 2010 (UTC)
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:39, 19 August 2010 | | 455 × 433 (36 KB) | Paolo.dL (talk | contribs) | Adding names of commas (diaschisma, lesser diesis) |
| 20:07, 29 July 2010 |  | 455 × 433 (35 KB) | Paolo.dL (talk | contribs) | Using as reference for minor sevenths the ratio 9/5 (C-Bb), rather than 16/9. | |
| 10:54, 29 July 2010 |  | 455 × 433 (35 KB) | Paolo.dL (talk | contribs) | Improved color code. Also, the previous version showed the symmetric scale, rather than the asymmetric one. | |
| 23:47, 28 July 2010 |  | 456 × 416 (34 KB) | Paolo.dL (talk | contribs) | {{Information |Description={{en|1=Sizes in cents of the 144 intervals in the C-based 5-limit tuning system. The selected ratios are listed below. Bold font indicates just intervals. The values were accurately computed using Microsoft Excel, then rounded t |
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