上饶师范学院学报2024,Vol.44Issue(5) :57-65.DOI:10.3969/j.issn.1004-2237.2024.05.008

论五度相生律的严密逻辑结构

On the Rigorous Logical Structure of Pythagorean Tuning

苏前忠 熊华平
上饶师范学院学报2024,Vol.44Issue(5) :57-65.DOI:10.3969/j.issn.1004-2237.2024.05.008

论五度相生律的严密逻辑结构

On the Rigorous Logical Structure of Pythagorean Tuning

苏前忠 1熊华平2
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作者信息

  • 1. 上饶师范学院 音乐舞蹈学院,江西 上饶 334001
  • 2. 上饶师范学院 数学与计算机学院,江西 上饶 334001
  • 折叠

摘要

文章用严密的数学归纳法定义了"五度相生律",并科学地给出"生律次数"这个无限五度律最核心的概念.为适应任一律制中的各律必须限于一个八度之内这个最基本的律学"铁律",以严格的数学方式得到由五度律某一律的生律次数x 计算其"二倍音调节数"m 的公式.根据生律次数完全确定一律的音名、频率值和从基音 C到该律的音程的音程名,并提供四种方法精确计算该音程的音分值(精确到 0.001 音分)和频率(精确到 0.01 Hz).

Abstract

The article defines the"Pythagorean Tuning"by a rigorous mathematical induction method,and scientifical-ly gives it"number of times tuning is generated",which is the core concept of the infinite Five-degree Tunes;fol-lowing the most basic"iron law"of tuning that each tuning must be limited to one octave in any tuning law;calculat-ing the formula of its m(number of two-tone adjustments)with x(the number of times of tuning generation of one certain tune of Five-degree Tunes)obtained in a strict mathematical way;According to the"the number of times of tuning generation",the uniform pitch name,frequency value and interval name from the fundamental note C to the interval of the rhythm are completely determined,and four methods are provided to accurately calculate phonetic val-ue(accurate to 0.001 phonetic value)and frequency(accurate to 0.01 Hz)of the interval.

关键词

五度相生律/归纳定义/生律次数/向前生律/向后生律/二倍音调节数/音名/音程

Key words

Pythagorean Tuning/induction definition/number of times tuning is generated/tuning generated forward/tuning generated backward/number of two-tone adjustments/pitch name/interval

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出版年

2024
上饶师范学院学报
上饶师范学院

上饶师范学院学报

CHSSCD
影响因子:0.147
ISSN:1004-2237
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