Decimal: Difference between revisions
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'''Decimal''' is a temperament in both the [[dicot]] and [[semaphore]] families of temperaments. It is also [[hemipyth]], meaning that it has approximations of √2, √3, and √(3/2). It is special in that it is also an [[exotemperament]]. | '''Decimal''' is a temperament in both the [[dicot]] and [[semaphore]] families of temperaments. It is also [[hemipyth]], meaning that it has approximations of √2, √3, and √(3/2). It is special in that it is also an [[exotemperament]]. | ||
= Interval chain = | |||
In the following table, odd harmonics and subharmonics 1–7 are labeled in '''bold'''. | |||
{| class="wikitable center-1 center-2 center-3" | |||
! rowspan="2" | # | |||
! colspan="1" | Period 0 | |||
! colspan="1" | Period 1 | |||
|- | |||
! Approx. Ratios | |||
! Approx. Ratios | |||
|- | |||
| -2 | |||
| '''3/2''' | |||
| 21/20, 15/14 | |||
|- | |||
| -1 | |||
| 12/7, '''7/4''' | |||
| 6/5, '''5/4''' | |||
|- | |||
| 0 | |||
| '''1/1''' | |||
| 7/5, 10/7 | |||
|- | |||
| 1 | |||
| '''8/7''', 7/6 | |||
| '''8/5''', 5/3 | |||
|- | |||
| 2 | |||
| '''4/3''' | |||
| 28/15, 40/21 | |||
|} | |||
One can see that the 10-note MOS of the '''decimal''' temperament contains the 7-odd-limit [[tonality diamond]]. | |||
Revision as of 02:34, 5 July 2024
Decimal is a temperament in both the dicot and semaphore families of temperaments. It is also hemipyth, meaning that it has approximations of √2, √3, and √(3/2). It is special in that it is also an exotemperament.
Interval chain
In the following table, odd harmonics and subharmonics 1–7 are labeled in bold.
| # | Period 0 | Period 1 |
|---|---|---|
| Approx. Ratios | Approx. Ratios | |
| -2 | 3/2 | 21/20, 15/14 |
| -1 | 12/7, 7/4 | 6/5, 5/4 |
| 0 | 1/1 | 7/5, 10/7 |
| 1 | 8/7, 7/6 | 8/5, 5/3 |
| 2 | 4/3 | 28/15, 40/21 |
One can see that the 10-note MOS of the decimal temperament contains the 7-odd-limit tonality diamond.